Write the Fraction in Simplest Form ((4yh^3)^-5)/(20h^-4)

$\frac{{(4 y h^{3})}^{- 5}}{20 h^{- 4}}$

Step 1

Move ${(4 y h^{3})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{20 h^{- 4} {(4 y h^{3})}^{5}}$

Step 2

Move $h^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{h^{4}}{20 {(4 y h^{3})}^{5}}$

Step 3

Simplify the denominator.

Apply the product rule to $4 y h^{3}$ .

$\frac{h^{4}}{20 {(4 y)}^{5} {(h^{3})}^{5}}$

Apply the product rule to $4 y$ .

$\frac{h^{4}}{20 (4^{5} y^{5}) {(h^{3})}^{5}}$

Raise $4$ to the power of $5$ .

$\frac{h^{4}}{20 (1024 y^{5}) {(h^{3})}^{5}}$

Multiply the exponents in ${(h^{3})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{h^{4}}{20 (1024 y^{5}) h^{3 \cdot 5}}$

Multiply $3$ by $5$ .

$\frac{h^{4}}{20 (1024 y^{5}) h^{15}}$

$\frac{h^{4}}{20 \cdot 1024 y^{5} h^{15}}$

Multiply $20$ by $1024$ .

$\frac{h^{4}}{20480 y^{5} h^{15}}$

Step 4

Cancel the common factor of $h^{4}$ and $h^{15}$ .

Multiply by $1$ .

$\frac{h^{4} \cdot 1}{20480 y^{5} h^{15}}$

Cancel the common factors.

Factor $h^{4}$ out of $20480 y^{5} h^{15}$ .

$\frac{h^{4} \cdot 1}{h^{4} (20480 y^{5} h^{11})}$

Cancel the common factor.

$\frac{h^{4} \cdot 1}{h^{4} (20480 y^{5} h^{11})}$

Rewrite the expression.

$\frac{1}{20480 y^{5} h^{11}}$