What is ((a^3*a)/(a^2))^{-1} ?

The solution to ((a^3*a)/(a^2))^{-1} is 1/(a^2)

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simplify ((a^3*a)/(a^2))^{-1}

simplify

(\frac{a ^{3} \cdot a}{a ^{2}})^{- 1}

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

Solution steps

(\frac{a ^{3} a}{a ^{2}})^{- 1}

Apply exponent rule:

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

(\frac{a ^{3} a}{a ^{2}})^{- 1} = \frac{1}{\frac{a ^{3} a}{a ^{2}}}

= \frac{1}{\frac{a ^{3} a}{a ^{2}}}

\frac{a ^{3} a}{a ^{2}} = \frac{a ^{4}}{a ^{2}}

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Apply exponent rule:

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

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

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

Subtract the numbers:

4 - 2 = 2

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

\frac{12}{14}

49 \times 7

1 - 81 p^{10}

49%

\frac{3}{48}