(a^5b^3/ab)^-1/3

Answer 1

To simplify this expression, we first need to distribute the exponent of -1/3 to all the terms inside the parentheses.

Recall that when we raise a product to a power, we can distribute the power to each individual factor. So, we have:

(a^5b^3/ab)^-1/3 = a^(5*-1/3) * b^(3*-1/3) * (1/a)^(-1/3)

Simplifying the exponents, we get:

a^(-5/3) * b^(-1) * (1/a)^(-1/3)

Now, we simplify the expression by combining like terms:

a^(-5/3) * b^(-1) * (1/a)^(-1/3)
= a^(-5/3) * b^(-1) * a^(1/3)
= a^(-5/3 + 1/3) * b^(-1)
= a^(-4/3) * b^(-1)
= b^(-1) / a^(4/3)
= b/a^(4/3)

Therefore, (a^5b^3/ab)^-1/3 simplifies to b/a^(4/3).