Question

simplify the expression using the rules for exponents
(a^1b^3) ^3/4 / (ab)^-3/4

Answer 1

For starters, we can see that a^1 is a.
Let's start with numerator:
(ab^3)^(3/4)
A property of exponents is that (ab)^x = a^x * b^x
So we get:
a^(3/4) * b (9/4)

Onto the denominator:
Apply the same rule:
a^(-3/4) * b^(-3/4)

Put the back together:

(a^(3/4) * b^(9/4))/
(a^(-3/4) * b^(-3/4)

Applying the property that (a^x)/(a^y) = a^(x - y) and the properties of fractions where (ab/cd = a/c * b/d):

a^(6/8) * b^(3)