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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?
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?
Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)
Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}
Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?
Simplified: 40 - 10 - 5
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How to Solve Exponents: A Step-by-Step Guide with Examples
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
Understanding the Laws of Exponents
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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
Step 1: Enter an exponential expression below which you want to simplify. The exponent calculator simplifies the given exponential expression using the laws of exponents. Step 2: Click the blue arrow to submit. Choose "Simplify" from the topic selector and click to see the result in our Algebra Calculator! Examples Simplify Simplify Simplify
Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. ... You'll be able to enter math problems once our session is over. New Messages. User is Typing. Expert Macros. General Replies.
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.
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.
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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.
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.
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
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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 ...
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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?