Question

s the following fraction in simplest form nts.
$\frac{-3(h^{3}t^{-5})^{-3}}{6h^{4}}$

Explanation:

Step1: Simplify the numerator's power

First, apply the power rule \((a^m)^n = a^{m \times n}\) to \((h^3t^{-5})^{-3}\):
\((h^3t^{-5})^{-3} = h^{3 \times (-3)}t^{-5 \times (-3)} = h^{-9}t^{15}\)
Multiply by the coefficient:
\(-3 \times h^{-9}t^{15} = -3h^{-9}t^{15}\)

Step2: Simplify the fraction coefficients

Divide the numerical coefficients:
\(\frac{-3}{6} = -\frac{1}{2}\)

Step3: Simplify the \(h\) terms

Use the quotient rule \(a^m \div a^n = a^{m-n}\) for \(h\):
\(h^{-9} \div h^4 = h^{-9 - 4} = h^{-13} = \frac{1}{h^{13}}\)

Step4: Combine all simplified terms

Combine the coefficient, \(h\) term, and \(t\) term:
\(-\frac{1}{2} \times \frac{t^{15}}{h^{13}}\)

Answer:

\(-\frac{t^{15}}{2h^{13}}\)