Multiplying and Dividing Exponent Expressions

For this topic, you will need to know exponents.
To review the Exponent Basics topic, see here.

For exponent expressions with the same base, the following laws apply.

x^ax^b = x^{a + b} x^a ÷ x^b = x^{a - b}

Example 1: Division

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'

5^{^-12} ÷ 5^{^-13} Final Exponent: 5
Value:

The bases are 5 so we can apply the exponent division law.

5^{^-12} ÷ 5^{^-13} = 5 ^{( ^-12 - ^-13 )} = 5 ^{( ^-12 + 13 )} = 5 ¹ = 5

The answer is Final Exponent: 5
Value:

Example 2: Multiplication and Division

Find the final exponent and the value of the expression after the exponent has been evaluated. If the answer is a fraction, express it as 'numerator'/'denominator', i.e. '5/7'

4⁸ ÷ 4^{^-4} × 4^{^-9} Final Exponent: 4
Value:

All the bases are 4 so we can apply both the exponent multilication and division laws.

4⁸ ÷ 4^{^-4} × 4^{^-9} = 4 ^{( 8 - ^-4 + ^-9 )} = 4 ^{( 8 + 4 - 9 )} = 4 ³ = 64

The answer is Final Exponent: 4
Value:

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