Question

Simplify ( 81/256) 1/4​

Answer 1

$(\frac{81}{256} ) {}^{ \frac{1}{4} } = ( \frac{{3}^{4}}{ {4}^{4} } ) {}^{ \frac{1}{4} } \\ = \frac{{3}^{1}}{ {4}^{1} } \\ = \frac{3}{4 \: } \: answer$

Answer 2

Concept

A number 'a' raised to the power x is simply 'a' multiplied x times by itself.

For example, if x = 2, a^2 = a*a

Given

we are given a mathematical expression (81/256)^1/4​

Find

we need to simplify the given term

Solution

We have  

(81/256)^1/4​

Now, by observation we can see that 81 is equal to 3 multiplied 4 times by itself, that is, 3*3*3*3

thus,

81 = 3^4

and similarly, 256 is 4 multiplied 4 times by itself and thus can be written as 4*4*4*4

Thus,

256 = 4^4

Therefore the entire expression becomes

(81/256)^1/4​ = (3^4/4^4)^1/4

= (3/4)^4/4

= (3/4)^1

= 3/4

Thus, on simplifying, (81/256)^1/4​ becomes 3/4

#SPJ2