Question

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

Answer 1

Answer:

$a^2b^2$

Step-by-step explanation:

Given the algebraic expression:

$\dfrac{a^3b^{-2}}{ab^{-4}} , a\neq 0, b\neq 0$

We are required to eliminate the negative exponents and find the resulting expression.

Using the Negative Exponent Law of Indices: $x^{-y}=\dfrac{1}{x^y}$

Using the Division Law of Indices: $\dfrac{t^x}{t^y}=t^{x-y}$

Therefore:

$\dfrac{a^3b^{-2}}{ab^{-4}} = a^{3-1}\cdot b^{-2-(-4)}\\ Simplifying\\a^{3-1}\cdot b^{-2-(-4)}=a^2b^{-2+4}\\=a^2b^2\\Therefore:\\\dfrac{a^3b^{-2}}{ab^{-4}}=a^2b^2$

Answer 2

Answer:

D

Step-by-step explanation:

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