## Which shows the following expression after the negative exponents have been eliminated? a^3b^-2/ab^-4 Assume a can’t equal 0

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

in progress 0
2022-05-21T12:03:06+00:00 2 Answers 0

## Answers ( 2 )

1. Equivalent expressions are expressions of equal values.

The equivalent expression is [tex]mathbf{a^{2}b^{2}}[/tex]

The expression is given as:

[tex]mathbf{frac{a^3b^{-2}}{ab^{-4}}}[/tex]

Apply law of indices

[tex]mathbf{frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2–4}}[/tex]

Rewrite as:

[tex]mathbf{frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2+4}}[/tex]

So, we have:

[tex]mathbf{frac{a^3b^{-2}}{ab^{-4}} = a^{2}b^{2}}[/tex]

Hence, the equivalent expression is [tex]mathbf{a^{2}b^{2}}[/tex]

Read more equivalent expressions at:

https://brainly.com/question/15715866

The given expression [tex]frac{a^3}{ab^{-4}}[/tex] after the negative exponents have been eliminated becomes [tex]frac{a^3b^{4}}{ab^{2}}[/tex]

Step-by-step explanation:

Given expression [tex]frac{a^3b^{-2}}{ab^{-4}}[/tex]

We have to write expression after the negative exponents have been eliminated and a u2260 0 and b u2260 0.

Consider the given expression [tex]frac{a^3b^{-2}}{ab^{-4}}[/tex]

We have to eliminate the negative exponents,

Using property of exponents, [tex]x^{-m}=frac{1}{x^m}[/tex] we have ,

[tex]b^{-2}=frac{1}{b^2} b^{-4}=frac{1}{b^4}[/tex]

Substitute, we get,

[tex]frac{a^3}{ab^{-4}}[/tex] becomes [tex]frac{a^3b^{4}}{ab^{2}}[/tex]

Thus, the given expression [tex]frac{a^3}{ab^{-4}}[/tex] after the negative exponents have been eliminated becomes [tex]frac{a^3b^{4}}{ab^{2}}[/tex]