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Popular >

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

Solution

simplify

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

Solution

a^{8}

Solution steps

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

Apply rule:

(a) = a

(a^{- 1}) = a^{- 1}

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

Simplify

(a^{2})^{2} : a^{4}

= a^{4} (a^{3})^{2} (a^{- 1})^{2}

Simplify

(a^{3})^{2} : a^{6}

= a^{4} a^{6} (a^{- 1})^{2}

Simplify

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

= a^{4} a^{6} \frac{1}{a ^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

a^{4} a^{6} = a^{4 + 6}

= a^{4 + 6} \frac{1}{a ^{2}}

Add the numbers:

4 + 6 = 10

= a^{10} \frac{1}{a ^{2}}

Multiply fractions:

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

= \frac{1 \cdot a ^{10}}{a ^{2}}

Multiply:

1 \cdot a^{10} = a^{10}

= \frac{a ^{10}}{a ^{2}}

Apply exponent rule:

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

\frac{a ^{10}}{a ^{2}} = a^{10 - 2}

= a^{10 - 2}

Subtract the numbers:

10 - 2 = 8

= a^{8}

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Frequently Asked Questions (FAQ)

What is (a^2*a^3*(a^{-1}))^2 ?
The solution to (a^2*a^3*(a^{-1}))^2 is a^8