Which of the given options represents the exponential form of $\frac{1}{8} \times (3)^{- 3}$ ?

$6^{- 3}$

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$6^{3}$

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$3^{- 6}$

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$3^{6}$

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Solution

The correct option is A
$6^{- 3}$

$\frac{1}{8} \times (3)^{- 3}$

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

$= 2^{- 3} \times (3)^{- 3}$ $[∵ a^{- m} = \frac{1}{a^{m}}]$

$= (2 \times 3)^{- 3}$ $[∵ a^{m} \times b^{m} = (a \times b)^{m}]$

$= 6^{- 3}$

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Using laws of exponents, simplify and write the answer in exponential form:
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The exponential form of $\frac{1}{8} \times 3^{- 3}$ is given by which of the following expressions?

(\frac{1}{8}) \times {(3)}^{- 3}

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