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]
