Question

| find the value of (125)^-2/3 ×(625)^5/4 /(1/5)^-3​

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ \frac{ {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } }{ \displaystyle \sf{{ \bigg( \frac{1}{5} \bigg)}^{ - 3} }} }$

EVALUATION

$\displaystyle \sf{ \frac{ {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } }{ \displaystyle \sf{{ \bigg( \frac{1}{5} \bigg)}^{ - 3} }} }$

$\displaystyle \sf{ = \frac{ {( {5}^{3} )}^{ - \frac{2}{3} } \times {( {5}^{4} )}^{ \frac{5}{4} } }{ \displaystyle \sf{{ ( {5}^{ - 1} )}^{ - 3} }} }$

$\displaystyle \sf{ = \frac{ {(5)}^{ -3 \times \frac{2}{3} } \times {( 5 )}^{ 4 \times \frac{5}{4} } }{ \displaystyle \sf{{ ( 5)}^{ - 1 \times - 3} }} }$

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

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

$\displaystyle \sf{ = \frac{ {(5)}^{ 3 } }{ \displaystyle \sf{{ ( 5)}^{ 3} }} }$

$\displaystyle \sf{ = {5}^{3 - 3} }$

$\displaystyle \sf{ = {5}^{0} }$

$= 1$

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Answer 2

Answer:

Step-by-step explanation:

(5) ^ 3 x -2/3 x (5)^4 x 5/4 / (5)^3

5^-2 x 5^4  /  5^3

5^-2 + 4 -3

5 ^ 3-3

5^0

= 1

answer is 1

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