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Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

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Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

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How to Solve Exponents: A Step-by-Step Guide with Examples

Solve Exponents

Exponents, also known as powers or indices, are a fundamental concept in mathematics. It plays a crucial role in various fields, from basic arithmetic to advanced calculus. An exponent represents how many times a number, called the base, is multiplied by itself. To solve exponents involves understanding the properties of exponents, simplifying expressions, and performing operations with exponential terms. In this guide, we will walk you through the process of solving exponent problems using maths.ai as a teaching tool.

Understanding Exponents

Before we delve into solving exponents problems, let’s review the basics of exponents.

An exponent is usually written as a superscript number next to the base. For example, in the expression 2^3, 2 is the base, and 3 is the exponent. This means that 2 is multiplied by itself three times: 2 * 2 * 2 = 8.

Example 1: Simple Exponentiation

Let’s solve the problem: 4^2.

Step 1: Identify the base and the exponent.

Exponent: 2

Step 2: Apply the exponentiation rule.

4^2 = 4 * 4 = 16

Exponent Properties

Understanding exponent properties is essential for solving more complex exponent problems.

Property 1: Product of Powers

a^m * a^n = a^(m + n)

This property states that when you multiply two powers with the same base, you can add their exponents.

Example 2: Product of Powers

Solve the problem: 3^4 * 3^2.

Step 1: Identify the base and the exponents.

Exponent 1: 4

Exponent 2: 2

Step 2: Apply the product of powers property.

3^4 * 3^2 = 3^(4 + 2) = 3^6 = 729

Property 2: Quotient of Powers

a^m / a^n = a^(m – n)

This property states that when you divide two powers with the same base, you can subtract their exponents.

Example 3: Quotient of Powers

Solve the problem: 5^7 / 5^4.

Exponent 1: 7

Exponent 2: 4

Step 2: Apply the quotient of powers property.

5^7 / 5^4 = 5^(7 – 4) = 5^3 = 125

Property 3: Power of a Power

(a^m)^n = a^(m * n)

This property states that when you raise a power to another power, you can multiply the exponents.

Example 4: Power of a Power

Solve the problem: (2^3)^4.

Exponent: 4

Step 2: Apply the power of a power property.

(2^3)^4 = 2^(3 * 4) = 2^12 = 4096

Simplifying Exponential Expressions

Simplifying exponential expressions involves applying the properties of exponents to combine or rewrite terms for easier computation.

Example 5: Simplifying Exponential Expressions

Simplify the expression: 2^5 * 2^8 / 2^3.

Exponent 1: 5, Exponent 2: 8, Exponent 3: 3

Step 2: Apply the properties of exponents.

2^5 * 2^8 / 2^3 = 2^(5 + 8 – 3) = 2^10 = 1024

Operations with Exponential Terms

Performing operations with exponential terms involves applying the properties of exponents while considering addition, subtraction, multiplication, and division.

Example 6: Operations with Exponential Terms

Solve the expression: (4^3 * 4^2) / 4^4 + 4^1.

Step 1: Identify the base and the exponents for each term.

Term 1: 4^3 * 4^2,Term 2: 4^4, Term 3: 4^1

Step 2: Simplify each term using the properties of exponents.

Term 1: 4^3 * 4^2 = 4^(3 + 2) = 4^5, Term 2: 4^4, Term 3: 4^1

Step 3: Combine the terms using addition and subtraction.

(4^5 * 4^4) / 4^4 + 4^1 = 4^5 + 4^1

Step 4: Calculate the final result.

4^5 + 4^1 = 1024 + 4 = 1028

Exponents are a fundamental concept in mathematics that allows us to represent repeated multiplication in a concise form. By understanding the properties of exponents, simplifying expressions, and performing operations with exponential terms, you can confidently tackle various exponent problems. Remember to apply the rules systematically, and when in doubt, use tools maths.ai to assist you in your journey towards mastering exponents. With practice and a clear grasp of exponent principles, you’ll be well-equipped to solve more complex maths problems that involve exponents.

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How to Solve Algebraic Problems With Exponents

Last Updated: July 6, 2023 Fact Checked

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 75,810 times.

In algebra, the operations (adding, subtracting, multiplying, and dividing) performed on variables work the same as the operations performed on numbers. When performing these operations on exponents, however, the laws are different. By learning these special rules for exponents, you can easily simplify algebraic expressions that include them.

Solving a Problem with Exponents

Step 1 Address the order of operations.

Understanding the Laws of Exponents

Step 1 Solve expressions with a positive exponent.

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-x{^{2}}=-1(x\times x)=-x

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  • ↑ https://www.mathsisfun.com/operation-order-pemdas.html
  • ↑ https://content.nroc.org/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U11_L1_T2_text_final.html
  • ↑ https://www.mathsisfun.com/exponent.html
  • ↑ http://www.mathwarehouse.com/algebra/exponents/index.php
  • ↑ http://www.mathwarehouse.com/algebra/exponents/laws-of-exponents.php
  • ↑ http://www.mathsisfun.com/algebra/negative-exponents.html

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    Exponents problems we've solved Pre Algebra Algebra Pre Calculus Calculus Linear Algebra Arithmetic Simplify: (6+3)\cdot (10-7) (6+3)⋅(10−7) See answer › Negative numbers Simplify: \frac {-4} {9}-\frac {3} {-6} 9−4−−63 See answer › Linear inequalities 1 Solve for x: x-4\ge-6 x−4≥−6 See answer › Powers and roots 1 Simplify: \sqrt {36} 36

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    Use free step-by-step math solver for solving exponents problems. CameraMath is an essential learning and problem-solving tool for students! Just snap a picture of the question of the homework and CameraMath will show you the step-by-step solution with detailed explanations.

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    Exponents are an easy way to shorten the number of terms needed when we multiply a number or variable by itself. For example, if we wanted to multiply the number 3 3 five times, we could write: 3\times 3\times 3\times 3\times 3 3 × 3 × 3 × 3 × 3 Using exponents, however, we can write: {3}^ {5} 35 This means we're multiplying 3 by itself five times.

  12. Expressions with exponents

    Unit 2 Algebraic expressions. Unit 3 Linear equations and inequalities. Unit 4 Graphing lines and slope. Unit 5 Systems of equations. Unit 6 Expressions with exponents. Unit 7 Quadratics and polynomials. Unit 8 Equations and geometry. Course challenge. Test your knowledge of the skills in this course.

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    Free Exponents Powers calculator - Apply exponent rules to multiply exponents step-by-step

  14. 3 Ways to Solve Exponents

    Method 1 Solving Basic Exponents Download Article 1 Learn the correct words and vocabulary for exponent problems. When you have an exponent, like , you have two simple parts. The bottom number, here a 2, is the base. The number it is raised to, here a 3, is known as the exponent or power.

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    Problem Solver Subjects. Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects. Here are example math problems within each subject that can be input into the calculator and solved.

  16. How to Solve Exponents: A Step-by-Step Guide with Examples

    To solve exponents involves understanding the properties of exponents, simplifying expressions, and performing operations with exponential terms. In this guide, we will walk you through the process of solving exponent problems using maths.ai as a teaching tool. Understanding Exponents

  17. Exponential Equation Calculator

    To solve an exponential equation start by isolating the exponential expression on one side of the equation. Then, take the logarithm of both sides of the equation to convert the exponential equation into a logarithmic equation. The logarithm must have the same base as the exponential expression in the equation.

  18. Exponents: rules formulas and practice problems

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    Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ... Solve exponential equations using exponent properties (advanced) Rational exponents and radicals: FAQ. Math > ... One problem is is in step 4, you cannot factor out things using multiplication, factoring out is ...

  20. How to Solve Algebraic Problems With Exponents: 8 Steps

    1 Address the order of operations. Just like any problem in mathematics, an algebraic problem must be completed by the order of operations. You can use the phrase "Please Excuse My Dear Aunt Sally," or the acronym PEMDAS, to help you remember Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. [1]

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  22. Solving Problems with Exponents

    This problem tests your fluency with exponent rules, and gives you a helpful clue to guide you through using them. Here you may see that both 27 and 9 are powers of 3. . Then you can simplify those exponents to get . Since when you divide exponents of the same base you subtract the exponents, you now have. is a solution to the equation above?