Question

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

Answer 1

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