What is (6a)^{-1}\times (3a^{-2})^{-2} ?

The solution to (6a)^{-1}\times (3a^{-2})^{-2} is (a^3)/(54)

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simplify (6a)^{-1}\times (3a^{-2})^{-2}

simplify

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

\frac{a ^{3}}{54}

Solution steps

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

Apply exponent rule:

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

(6 a)^{- 1} = \frac{1}{6 a}

= \frac{1}{6 a} (3 a^{- 2})^{- 2}

Simplify

(3 a^{- 2})^{- 2} : \frac{a ^{4}}{9}

= \frac{1}{6 a} \cdot \frac{a ^{4}}{9}

Apply the fraction rule:

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

= \frac{1 \cdot a ^{4}}{6 a \cdot 9}

Apply rule:

1 \cdot a = a

1 \cdot a^{4} = a^{4}

= \frac{a ^{4}}{6 a \cdot 9}

Simplify

\frac{a ^{4}}{a} : a^{3}

= \frac{a ^{3}}{6 \cdot 9}

Multiply the numbers:

6 \cdot 9 = 54

= \frac{a ^{3}}{54}

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What is (6a)^{-1}\times (3a^{-2})^{-2} ?
The solution to (6a)^{-1}\times (3a^{-2})^{-2} is (a^3)/(54)