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# Working with Exponents Practice Questions

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Updated on Sep 23, 2011

## Introduction

In this set of practice questions, you will practice adding, subtracting, multiplying, and dividing expressions that contain variables with exponents. You will follow all the rules you have learned about operating with variables, but in this lesson, the variables have exponents.

## Tips for Working with Exponents

3n + 5n = 8n, or 5x2y – 3x2y = 2x2y.

When multiplying variables with exponents, if the variables are the same, add the exponents and write the base only once:

(a4)(a3) = a(4 + 3) = a7

(x2y3)(axy5) = ax(2 + 1)y(3 + 5) = ax3y8

When dividing variables with exponents, if the variables are the same, you subtract the exponents:

If the exponent of a similar term in the denominator is larger than the one in the numerator, the exponent will have a negative sign:

A negative numerator becomes positive when the variable is moved into the denominator.

When the result of a division leaves an exponent of zero, the term raised to the power of zero equals 1:

When a variable with an exponent is raised to a power, you multiply the exponent to form the new term:

(b2)3 = b2 · b2 · b2 = b(2 + 2 + 2) = b6

(2x2y)2 = 2x2y · 2x2y = 2 · 2 · x2 · x2 · y · y = 22x2 + 2y1 + 1 = 4x4y2

Remember order of operations: PEMDAS. Generally, list terms in order from highest power to lowest power.

## Practice Questions

Simplify the following expressions:

1. 5x2 + 8x2
2. 5ab4 – ab4
3. 9mn3 + 8mn + 2mn3
4. 5c2 + 3c – 2c2 + 4 – 7c
5. 3x2 + 4ax – 8a2 + 7x2 – 2ax + 7a2
6. (5n2)(2n5 – 2n3 + 3n7)
7. 5xy · 6xy + 7x2y2
8. (5a2 · 3ab) + 2a3b
9. (4a2)3 + (2a3)2 – 11a6
10. (3xy5)2 – 11x2y2(4y4)2
11. 4x–2(3ax)5
12. (5a2x3y)3
13. (ab2)3 + 2b2 – (4a)3b6

Numerical expressions in parentheses like this [ ] are operations performed on only part of the original expression. The operations performed within these symbols are intended to show how to evaluate the various terms that make up the entire expression.

Expressions with parentheses that look like this ( ) contain either numerical substitutions or expressions that are part of a numerical expression. Once a single number appears within these parentheses, the parentheses are no longer needed and need not be used the next time the entire expression is written.

When two pair of parentheses appear side by side like this ( )( ), it means that the expressions within are to be multiplied.

Sometimes parentheses appear within other parentheses in numerical or algebraic expressions. Regardless of what symbol is used, ( ), { }, or [ ], perform operations in the innermost parentheses first and work outward.

Underlined expressions show the simplified result.

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