# Which shows the following expression after the negative exponents have been eliminated?StartFraction a cubed b Superscript negative 2 Baseline Over

4 answers

###### Question:

Which shows the following expression after the negative exponents have been eliminated? StartFraction a cubed b Superscript negative 2 Baseline Over a b Superscript negative 4 Baseline EndFraction, a not-equals 0, b not-equals 0

## Answers

[tex]a^2b^2[/tex]

Step-by-step explanation:

Given the algebraic expression:

[tex]\dfrac{a^3b^{-2}}{ab^{-4}} , a\neq 0, b\neq 0[/tex]

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

Using the Negative Exponent Law of Indices: [tex]x^{-y}=\dfrac{1}{x^y}[/tex]

Using the Division Law of Indices: [tex]\dfrac{t^x}{t^y}=t^{x-y}[/tex]

Therefore:

[tex]\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[/tex]

Answer is D: a^3b^4/ab^2

Step-by-step explanation:

I took the test on Edge 2020 and this was the correct answer...

D

Step-by-step explanation:

did the quiz

The answer is C I think iam not sure about it

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