Simplify ((2a^4)^2)/(a^0a^5)

$\frac{{(2 a^{4})}^{2}}{a^{0} a^{5}}$

Step 1

Multiply $a^{0}$ by $a^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(2 a^{4})}^{2}}{a^{0 + 5}}$

Add $0$ and $5$ .

$\frac{{(2 a^{4})}^{2}}{a^{5}}$

Step 2

Simplify the numerator.

Apply the product rule to $2 a^{4}$ .

$\frac{2^{2} {(a^{4})}^{2}}{a^{5}}$

Raise $2$ to the power of $2$ .

$\frac{4 {(a^{4})}^{2}}{a^{5}}$

Multiply the exponents in ${(a^{4})}^{2}$ .

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

$\frac{4 a^{4 \cdot 2}}{a^{5}}$

Multiply $4$ by $2$ .

$\frac{4 a^{8}}{a^{5}}$

Step 3

Cancel the common factor of $a^{8}$ and $a^{5}$ .

Factor $a^{5}$ out of $4 a^{8}$ .

$\frac{a^{5} (4 a^{3})}{a^{5}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{a^{5} (4 a^{3})}{a^{5} \cdot 1}$

Cancel the common factor.

$\frac{a^{5} (4 a^{3})}{a^{5} \cdot 1}$

Rewrite the expression.

$\frac{4 a^{3}}{1}$

Divide $4 a^{3}$ by $1$ .

$4 a^{3}$