Question

Simplify each expression.

Answer 1

Step-by-step explanation:

remember that x^-n means 1/(x^n).

x^a × x^b = x^(a+b)

x^a / x^b = x^(a-b)

(x^a)^b = x^(a×b)

(x×y)^n = x^n × y^n

so,

a^2 / a^-2 = a^(2 - -2) = a^4

and

b^-3 / b^2 = b^(-3 - 2) = b^-5 = 1/(b^5)

that means we have then :

(a^4 × b^-5)^2 = (a^4)^2 × (b^-5)^2 = a^8 × b^-10 =

= a^8 / b^10 = a⁸/b¹⁰