rewrite the expression in the form $z^n$. \n$left(z^{-\frac{4}{3}}\right)^{-\frac{6}{5}} = $
rewrite the expression in the form $z^n$. \n$left(z^{-\frac{4}{3}}\right)^{-\frac{6}{5}} = $
Answer
Explanation:
Step1: Recall the power of a power rule
When we have ((a^m)^n), we multiply the exponents, so ((a^m)^n = a^{m\times n}). Here, (a = z), (m = -\frac{4}{3}), and (n = -\frac{6}{5}).
Step2: Multiply the exponents
We need to calculate (\left(-\frac{4}{3}\right)\times\left(-\frac{6}{5}\right)). First, multiply the numerators: ((-4)\times(-6)=24). Then multiply the denominators: (3\times5 = 15). So we have (\frac{24}{15}), which simplifies to (\frac{8}{5}) (dividing numerator and denominator by 3).
Answer:
(z^{\frac{8}{5}})