Question

The value of (625)^3/4

Answer 1

(625)^¾

= (5×5×5×5)^¾

= [ (5)^4 ]^¾

= 5³ = 125

Answer 2

$\displaystyle \sf{ {(625)}^{ \frac{3}{4} } } = 125$

Given :

The expression $\displaystyle \sf{ {(625)}^{ \frac{3}{4} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down 625 in exponent form

On prime factorisation of 625 we get

625 = 5 × 5 × 5 × 5

∴ 625 = 5⁴

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {(625)}^{ \frac{3}{4} } }$

$\displaystyle \sf{ = {( {5}^{4} )}^{ \frac{3}{4} } }$

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

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

$\displaystyle \sf{ =125}$

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