ChasLynne
contestada

Which shows the following expression after the negative exponents have been eliminated?
a^3b^-2/ab^-4
Assume a can’t equal 0 and b can’t equal 0

Respuesta :

Answer:

The given expression  [tex]\frac{a^3}{ab^{-4}}[/tex] after the negative exponents have been eliminated becomes [tex]\frac{a^3b^{4}}{ab^{2}}[/tex]

Step-by-step explanation:

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

We have to write expression after the negative exponents have been eliminated and  a ≠ 0 and b ≠ 0.

Consider the given expression [tex]\frac{a^3b^{-2}}{ab^{-4}}[/tex]  

We have to eliminate the negative exponents,

Using  property of exponents, [tex]x^{-m}=\frac{1}{x^m}[/tex]  we have ,

[tex]b^{-2}=\frac{1}{b^2} \\\\b^{-4}=\frac{1}{b^4}[/tex]

Substitute, we get,

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

Thus, the given expression  [tex]\frac{a^3}{ab^{-4}}[/tex] after the negative exponents have been eliminated becomes [tex]\frac{a^3b^{4}}{ab^{2}}[/tex]

MrRoyal

Equivalent expressions are expressions of equal values.

The equivalent expression is [tex]\mathbf{a^{2}b^{2}}[/tex]

The expression is given as:

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

Apply law of indices

[tex]\mathbf{\frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2--4}}[/tex]

Rewrite as:

[tex]\mathbf{\frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2+4}}[/tex]

So, we have:

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

Hence, the equivalent expression is [tex]\mathbf{a^{2}b^{2}}[/tex]

Read more equivalent expressions at:

https://brainly.com/question/15715866

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