Question

if root 256÷ root x =1/5 then the value of x is .


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Answer 1

Answer---->

6400

Step-by-step explanation:

Given-----> √256 ÷ √x = 1/5

To find ------> Value of x

Solution-----> First we do prime factorization of 256

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2⁸

√256 = √( 2⁸ )

= ( 2⁸ )¹/²

We have a law of exponent as follows ,

( aᵐ )ⁿ = aᵐⁿ , applying it here we get,

= 2⁸ ˣ ¹/²

= 2⁴

= 2 × 2 × 2 × 2

√256 = 16

Now returning to original problem , we get,

√256 ÷ √x = 1/5

=> 16 × ( 1 / √x ) = 1/5

=> 16 / √x = 1 / 5

=> √x = 16 × 5

=> √x = 80

Squaring both sides we get,

=> ( √x )² = ( 80 )²

=> ( x¹/² )² = 80 × 80

=> x = 6400

Additional information----->

1) aᵐ aⁿ = aᵐ⁺ⁿ

2) aᵐ ÷ aⁿ = aᵐ⁻ⁿ

3) a⁻ᵐ = 1 / aᵐ

4) a⁰ = 1

5) ( aᵐ )ⁿ = aᵐⁿ

Answer 2

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(256/x) ^1/2=2

squaring both side

256/x=4

x=256÷4

x=64