Question

the reciprocal of 3 upon 2 raise to 5 the answer is 3 upon 2 raise to -5 how ?
please help me​

Answer 1

Step-by-step explanation:

According to powers and exponets law , If any number is raised to its negative power , the answer becomes its reciprocal .

For Eg. :

${2 }^{ - 2}$

=

$\frac{1}{2 {}^{2} }$

So , similarly ,

According to your question ,

$( \frac{3}{2}) {}^{5}$

The reciprocal should be (2/3) to power 5

But , According to exponents law

If we write (3/2) raise to power -5 which is negative

will be equal

to (2/3) to power 5 only .

Hope you go it the answer you were looking for...!

Answer 2

Answer:

According to you

${ (\frac{2}{3}) }^{5}= {(\frac{3}{2})}^{ - 5}$

Let's prove this

${ (\frac{2}{3}) }^{5} \\ = {(\frac{2}{1} \times \frac{1}{3} )}^{5} \\ = {(( { \frac{1}{2} })^{ - 1} \times {3}^{ - 1} )}^{5} \\ = {((\frac{3}{2} )^{ - 1} )}^{5} \\ = ( \frac{3}{2} )^{ ( - 1 \times 5)} \\ = ( {\frac{3}{2} })^{ - 5} = rhs$

Hope it helps.