Question

The number (256)^5/7 is _____ root of ____ power of _____ ?
a) 7th ; 5th; 256
b) 5th ;7th ; 256
c) 256th ; 5th; 7
d) 7th ;256th; 5

Answer 1

Answer:

It is known that,

nth root of a is expressed as a1/n.

(1) Fifth root of 13

= (13)1/5

(2) Sixth root of 9

= (9)1/6

(3) Square root of 256

= (256)1/2

(4) Cube root of 17

= (17)1/3

(5) Eighth root of 100

= (100)1/8

(6) Seventh root of 30

= (30)1/7

Answer 2

Given : The number (256)^5/7 is _____ root of ____ power of _____ ?

$(256)^{\frac{5}{7} }$

To Find :  Fill in the blank

a) 7th ; 5th; 256

b) 5th ;7th ; 256

c) 256th ; 5th; 7

d) 7th ;256th;

Solution:

xᵃᵇ = (xᵃ)ᵇ

$\sqrt[n]{x} =x^{\frac{1}{n} }$

$(256)^{\frac{5}{7} }=\sqrt[7]{(256)^{5}}$

$\sqrt[n]{x}$  = nth root of x

xⁿ  = nth power of x

256⁵  = 5th power of  256

$\sqrt[7]{(256)^{5}}$ =  7th root of 256⁵

Hence   7th root of  5th power of  256

The number $(256)^{\frac{5}{7} }$  is 7th root of  5th  power of 256

Correct option is a)  7th ; 5th; 256

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