What is 7a^{-3}*b^{-5} ?

The solution to 7a^{-3}*b^{-5} is 7/(a^3b^5)

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simplify 7a^{-3}*b^{-5}

simplify

7 a^{- 3} \cdot b^{- 5}

\frac{7}{a ^{3} b ^{5}}

Solution steps

7 a^{- 3} b^{- 5}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

a^{- 3} = \frac{1}{a ^{3}}

= 7 \cdot \frac{1}{a ^{3}} b^{- 5}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

b^{- 5} = \frac{1}{b ^{5}}

= 7 \cdot \frac{1}{a ^{3}} \cdot \frac{1}{b ^{5}}

Apply the fraction rule:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{7 \cdot 1 \cdot 1}{a ^{3} b ^{5}}

Multiply the numbers:

7 \cdot 1 \cdot 1 = 7

= \frac{7}{a ^{3} b ^{5}}

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