Question

(256x^16/81y^4)^-1/4​

Answer 1

may be that is correct but please check it

Answer 2

The answer is 3y/4x⁴

GIVEN

Algebraic equation;

$( \frac{ {256x}^{16} }{ {81y}^{4} } ) ^{ - \frac{1}{4} }$

TO FIND

To simplify the given term

SOLUTION

The above problem can be simply solved as follows;

It is known that,

(a/b)⁻ᵐ = (b/a)ᵐ

Therefore,

$( \frac{ {256x}^{16} }{ {81y}^{4} } ) ^{ - \frac{1}{4} } = ( \frac{{81y}^{4} }{ {256x}^{16} } )^{ \frac{1}{4} }$

Now,

81y⁴ can be written as (3)⁴.(y⁴)

Also,

256x¹⁶ can be written as (4)⁴.(x⁴)⁴

Now,

(a)ᵐ × (b)ᵐ = (ab)ᵐ

Therefore,

(3)⁴.(y)⁴ = (3y)⁴

(4)⁴.(x⁴)⁴ = (4x)⁴

Now,

The equation becomes;

$= ( \frac{3y^{4} }{4 {( x^{4} ) }^{4} } )^{ \frac{1}{4} }$

This can also be written as;

$= (( \frac{3y}{4x ^{4} } )^{4})^{ \frac{1}{4} }$

Now,

$= (( \frac{3y}{4x ^{4} } )^{4})^{ \frac{1}{4} } = ( \frac{3y}{4x^{4} } )^{4} \times ^{ \frac{1}{4} }$

= 3y/4x⁴

Hence, The answer is 3y/4x⁴