Let's start with the given expression:
[tex]\[ h^4 \left( h^3 \right)^{-6} \][/tex]
To simplify the expression step-by-step:
1. Simplify the powers inside the parenthesis:
[tex]\[\left(h^3\right)^{-6}\][/tex]
Recall that [tex]\(\left(a^m\right)^n = a^{mn}\)[/tex]. Applying this rule, we get:
[tex]\[\left(h^3\right)^{-6} = h^{3 \cdot (-6)} = h^{-18}\][/tex]
2. Combine the two expressions:
Now substitute [tex]\(h^{-18}\)[/tex] back into the original expression:
[tex]\[h^4 \cdot h^{-18}\][/tex]
3. Use the property of exponents:
When you multiply expressions with the same base, you add the exponents: [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]. Applying this rule, we get:
[tex]\[h^4 \cdot h^{-18} = h^{4 + (-18)}\][/tex]
Simplify the exponent:
[tex]\[h^{4 - 18} = h^{-14}\][/tex]
The simplified form of the expression is:
[tex]\[h^{-14}\][/tex]
Given the multiple choice options, we rewrite [tex]\(h^{-14}\)[/tex] in a more recognizable form:
[tex]\[h^{-14} = \frac{1}{h^{14}}\][/tex]
Thus, the simplified expression corresponds to:
[tex]\[\boxed{\frac{1}{h^{14}}}\][/tex]
