Choose the correct simplification of the expression [tex]\frac{4b}{a^{-10}}[/tex].

A. [tex]\frac{a^{10} b}{4}[/tex]

B. [tex]4 a^{10} b[/tex]

C. [tex]\frac{4}{a^{10} b}[/tex]

D. Already simplified



Answer :

To simplify the expression [tex]\(\frac{4b}{a^{-10}}\)[/tex]:

1. Identify the negative exponent property:
Recall that [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. Hence, [tex]\(a^{-10} = \frac{1}{a^{10}}\)[/tex].

2. Rewrite the expression using the property:
Substituting [tex]\(a^{-10}\)[/tex] with [tex]\(\frac{1}{a^{10}}\)[/tex] in the denominator, the expression [tex]\(\frac{4b}{a^{-10}}\)[/tex] can be rewritten as:
[tex]\[ \frac{4b}{\frac{1}{a^{10}}} \][/tex]

3. Simplify the complex fraction:
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, dividing by [tex]\(\frac{1}{a^{10}}\)[/tex] is the same as multiplying by [tex]\(a^{10}\)[/tex]:
[tex]\[ \frac{4b}{\frac{1}{a^{10}}} = 4b \cdot a^{10} \][/tex]

4. Combine the terms:
Write the simplified form by combining the constants and variables:
[tex]\[ 4b \cdot a^{10} = 4a^{10}b \][/tex]

So, the correct simplification of the expression [tex]\(\frac{4b}{a^{-10}}\)[/tex] is:

[tex]\[ 4a^{10}b \][/tex]

Hence, the correct answer is:

[tex]\[4a^{10}b\][/tex]