Question

Which shows the following expression after the negative exponents have been eliminated?

a^3b^-2/ab^-4
Assume a can’t equal 0 and b can’t equal 0

Answer 1

The given expression
`(a^3)/(ab^(-4))` after the negative exponents have been eliminated becomes
`(a^3b^(4))/(ab^(2))`

Explanation:

Given expression
`(a^3b^(-2))/(ab^(-4))`

We have to write expression after the negative exponents have been eliminated and a ≠ 0 and b ≠ 0.

Consider the given expression
`(a^3b^(-2))/(ab^(-4))`

We have to eliminate the negative exponents,

Using property of exponents,
`x^(-m)=(1)/(x^m)` we have ,

`b^(-2)=(1)/(b^2) \\\\b^(-4)=(1)/(b^4)`

Substitute, we get,

`(a^3)/(ab^(-4))` becomes
`(a^3b^(4))/(ab^(2))`

Thus, the given expression
`(a^3)/(ab^(-4))` after the negative exponents have been eliminated becomes
`(a^3b^(4))/(ab^(2))`