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givi [52]
2 years ago
12

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

Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
7 0

Answer:

\frac{a^3b^4}{ab^2} which is the last choice in the question

Step-by-step explanation:

Simplify

\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}

Using the fact that \frac{x^m}{x^n}  =x^{m-n}

We get

\frac{a^3}{a} = a^{3-1} = a^2

\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2

So

\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2

Multiplying numerator and denominator by ab^2 gives

a^2b^2 \frac{ab^2}{ab^2}

= \frac{a^3b^4}{ab^2} ANSWER

Hint:

We can eliminate first choice since negative exponents still remain

We can eliminate third choice because the expression has a minus sign which is not possible

That just leaves second and fourth choices to work with

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