Question

125-1/3[125 1/3-125 2/3]

Answer 1

Hey friend,
Here is the answer you were looking for:
${125}^{ - \frac{1}{3} } ( {125}^{ \frac{1}{3} } - {125}^{ \frac{2}{3} } ) \\ \\ = {125}^{ - \frac{1}{3} } \times {125}^{ \frac{1}{3} } - {125}^{ - \frac{1}{3} } \times {125}^{ \frac{2}{3} }$

Using the identity :
${a}^{x} \times {a}^{y} = {a}^{x + y}$
$= {125}^{ - \frac{1}{3} + \frac{1}{3} } - {125}^{ - \frac{1}{3} + \frac{2}{3} } \\ \\ = {125}^{0} - {125}^{ \frac{ - 1 + 2}{3} } \\ \\ = 1 - {125}^{ \frac{1}{3} } \\ \\ = 1 - {5}^{3 \times \frac{1}{3} } \\ \\ = 1 - 5 \\ \\ = - 4$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺

Answer 2

Given: Here we have given the equation  ${125}^{ - \frac{1}{3} } ( {125}^{ \frac{1}{3} } - {125}^{ \frac{2}{3} } )$

To find: we have to find the equivalent answer ${125}^{ - \frac{1}{3} } ( {125}^{ \frac{1}{3} } - {125}^{ \frac{2}{3} } )$

Solution:

Here we have given the equation

${125}^{ - \frac{1}{3} } ( {125}^{ \frac{1}{3} } - {125}^{ \frac{2}{3} } ) \\ \\ = {125}^{ - \frac{1}{3} } \times {125}^{ \frac{1}{3} } - {125}^{ - \frac{1}{3} } \times {125}^{ \frac{2}{3} }$

we will use the identity :

${a}^{x} \times {a}^{y} = {a}^{x + y} = {125}^{ - \frac{1}{3} + \frac{1}{3} } - {125}^{ - \frac{1}{3} + \frac{2}{3} } \\ \\ = {125}^{0} - {125}^{ \frac{ - 1 + 2}{3} } \\ \\ = 1 - {125}^{ \frac{1}{3} } \\ \\ = 1 - {5}^{3 \times \frac{1}{3} } \\ \\ = 1 - 5 \\ \\ = - 4$

Final answer:

Hence the answer is -4