What is the simplified form of the expression? k^3{k^7/5}^-5

a. k^1/4
b. 1/k^4
c. k^4
d. 1/k^1/4

B

k^-4= 1 / k^4

Step-by-step explanation:

The expression is

k^3{k^7/5}^-5

To simplify the expression, we take the following steps.

Recall the following laws of indices

a^x + a ^y = a ^ (x+y) - - - - - - - - - -1

(a^x)^y = a^(x×y) = a^ xy - - - - - - - 2

a ^-x = 1 / a^ x - - - - - - - - - - - - - - - 3

Applying these laws of indices, we have

k^3{k^7/5}^-5

(applying law 2), we have

= k^3{k^7/5× -5}

= {k^3{k^7×-1} = {k^3{k^-7}

(applying law 1 )

k^3(k^-7) = k^ (3+ -7) = k ^3-7 = k^-4

Applying law 3,

k^-4= 1 / k^4

a² + b²= c²

24² + 7² = c²

c= 25