Question

find the reciprocal of (2/3) power 4

Answer 1

$= (\frac{2}{3})^{4}$
$= \frac{2 ^{4} }{3^{4} }$
$= \frac{16}{81}$
$and \: its \: reciprocal \: is \: \frac{81}{16}$

Answer 2

Given:

A fraction=2/3

To find:

The reciprocal of (2/3) raised to the power 4

Solution:

The reciprocal of (2/3) raised to the power 4 is 81/16.

We can find the solution by following the given process-

We know that the reciprocal of a number is obtained by reversing the numerator and denominator of a fraction.

The given fraction is 2/3.

So, the reciprocal of 2/3=3/2

Now, we have to raise the reciprocal to power 4.

We will have to multiply the obtained fraction by itself four times.

So, 3/2 raised to the power 4= $(3/2)^{4}$

=3/2×3/2×3/2×3/2

=3×3×3×3/2×2×2×2

=$3^{4}$/$2^{4}$

=81/16

Therefore, the reciprocal of (2/3) raised to the power 4 is 81/16.