Question

the reciprocal of 2/5 power -1

Answer 1

The reciprocal of
${ \frac{2}{5} }^{ - 1}$
is
${ \frac{5}{2} }^{ - 1}$
and after eliminating the power. The answer is
$\frac{2}{5}$

Answer 2

Answer:

the reciprocal of 2/5 power -1 is $\frac{2}{5}$

Step-by-step explanation:

Here we want to find reciprocal of 2/5 power -1

2/5 power -1 means ${ (\frac{2}{5} )}^{ - 1}$

We know x is a number then ${x}^{ - 1} = \frac{1}{x}$

Here

${ (\frac{2}{5} )}^{ - 1} \\ = \frac{1}{ \frac{2}{5} } \\ = 1 \times \frac{5}{2} \\ = \frac{5}{2}$

We know reciprocal of y$= \frac{1}{y}$

Now reciprocal of 2/5 power -1 = reciprocal of

$\frac{5}{2}$ is $\frac{1}{ \frac{5}{2} } = \frac{2}{5}$

Therefore the reciprocal of 2/5 power -1 is $\frac{2}{5}$

It is a problem of Power of indices.

Some important formulas of power of indices

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$