Question

Evaluate (3/5)²×(3/5)-³×(3/5)³​

Answer 1

Answer:

To solve :  (3/5)²×(3/5)-³×(3/5)³​

according to first law of indices If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

In general : $x^{m} \times x^{n} = x^{m + n}$

Therefore , we can rewrite the given question :  (3/5)²×(3/5)-³×(3/5)³​

as , $(\frac{3}{5}) ^{2 - 3 + 3}$

on solving we get, $(\frac{3}{5}) ^{2}$

                =   $\frac{3}{5} \times \frac{3}{5}$

                =     $\frac{9}{25}$

               

hence , 9/ 25 is the required answer .

Answer 2

Given expression is

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

As we from the laws of indices,

The formula which can be used is

$a^{m} \times a^{n} \times a^{p} =a^{m+n+p}$

Here,

$a=\frac{3}{5}$

$m=2,\\n=-3\\p=3$

substitute these values in the formula.

We get,

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

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

$\frac{9}{25}$

Therefore, the value of  $(\frac{3}{5}) ^{2} \times(\frac{3}{5}) ^{-3} \times(\frac{3}{5} )^{3}$ after evaluation is $\frac{9}{25}$.