What is a^{-4}b^{-1/2} ?

The solution to a^{-4}b^{-1/2} is 1/(a^4b^{1/2)}

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simplify a^{-4}b^{-1/2}

simplify

a^{- 4} b^{- \frac{1}{2}}

\frac{1}{a ^{4} b ^{\frac{1}{2}}}

Solution steps

a^{- 4} b^{- \frac{1}{2}}

Apply exponent rule:

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

a^{- 4} = \frac{1}{a ^{4}}

= \frac{1}{a ^{4}} b^{- \frac{1}{2}}

Apply exponent rule:

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

b^{- \frac{1}{2}} = \frac{1}{b ^{\frac{1}{2}}}

= \frac{1}{a ^{4}} \cdot \frac{1}{b ^{\frac{1}{2}}}

Apply the fraction rule:

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

= \frac{1 \cdot 1}{a ^{4} b ^{\frac{1}{2}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{a ^{4} b ^{\frac{1}{2}}}

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