Question

find value 625 power 1 by 4

Answer 1

We know that,
625^1/4
25^1/2
=5

Answer 2

$\displaystyle \sf{ {(625)}^{ \frac{1}{4} } } = 5$

Given :

The expression

$\displaystyle \sf{ {(625)}^{ \frac{1}{4} } }$

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

$\displaystyle \sf{ {(625)}^{ \frac{1}{4} } }$

$\displaystyle \sf{ = {( {5}^{4} )}^{ \frac{1}{4} } }$

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

$\displaystyle \sf{ = {(5)}^{1 } }$

$\displaystyle \sf{ =5}$

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