Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{4h^{-10}}{(4h^{5})^{2}}\\)

Explanation:

Step1: Expand denominator's exponent

$(4h^5)^2 = 4^2 \cdot (h^5)^2 = 16h^{10}$

Step2: Rewrite negative exponent

$4h^{-10} = \frac{4}{h^{10}}$

Step3: Rewrite the original fraction

$\frac{\frac{4}{h^{10}}}{16h^{10}} = \frac{4}{h^{10} \cdot 16h^{10}}$

Step4: Simplify coefficients and exponents

$\frac{4}{16h^{20}} = \frac{1}{4h^{20}}$

Answer:

$\frac{1}{4h^{20}}$