To simplify the expression [tex]\(\frac{9}{h^{-3}}\)[/tex], let's follow these steps:
1. Understand the property of exponents: Recall that a negative exponent means taking the reciprocal of the base. Specifically, [tex]\( x^{-a} = \frac{1}{x^a} \)[/tex].
2. Apply this property to our expression: We have [tex]\( h^{-3} \)[/tex] in the denominator. We can rewrite [tex]\( h^{-3} \)[/tex] as follows:
[tex]\[
h^{-3} = \frac{1}{h^3}
\][/tex]
3. Substitute [tex]\( h^{-3} \)[/tex] in the expression:
[tex]\[
\frac{9}{h^{-3}} = \frac{9}{\frac{1}{h^3}}
\][/tex]
4. Simplify the fraction: When we divide by a fraction, it is equivalent to multiplying by its reciprocal:
[tex]\[
\frac{9}{\frac{1}{h^3}} = 9 \times h^3
\][/tex]
5. Write the final expression:
[tex]\[
9 \times h^3 = 9h^3
\][/tex]
Thus, the correct simplification of the expression [tex]\(\frac{9}{h^{-3}}\)[/tex] is:
[tex]\[
9h^3
\][/tex]
Therefore, the correct choice is:
[tex]\[
9 h^3
\][/tex]
