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


Which Shows The Following Expression After The Negative Exponents Have Been Eliminated class=

Sagot :

Answer:

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

Step-by-step explanation:

Simplify

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

Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]

We get

[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]

[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]

So

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

Multiplying numerator and denominator by [tex]ab^2[/tex] gives

[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]

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