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Which expression is equivalent to 81?

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2^{9}

{(\frac{1}{3})}^{- 4}

3^{- 4}

{(\frac{1}{3})}^{4}

answer is B.

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Detailed Solution

It is given the options
1)

2^{9}

,
2)

{(\frac{1}{3})}^{- 4}

,
3)

3^{- 4}

,
4)

{(\frac{1}{3})}^{4}

.
Checking for option 1.
Simplifying

2^{9}

2^{9}

=512
Checking for option 2.
Given,

{(\frac{1}{3})}^{- 4}

.
We know that,

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

Therefore,

({\frac{1}{3})}^{- 4}

= 3^{4}

= 81

Checking for option 3.
Given,

3^{- 4}

.
We know that,

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

3^{- 4} = \frac{1}{3^{4}}

= \frac{1}{81}

Checking for option 4.
Given,

{(\frac{1}{3})}^{4} .

= \frac{1}{81}

So the correct option is 2.

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