Simplify (4a^2(a^3))/(16b(b^2))

$\frac{4 a^{2} (a^{3})}{16 b (b^{2})}$

Step 1

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$\frac{4 (a^{3} a^{2})}{16 b (b^{2})}$

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

$\frac{4 a^{3 + 2}}{16 b (b^{2})}$

Add $3$ and $2$ .

$\frac{4 a^{5}}{16 b (b^{2})}$

Step 2

Multiply $b$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$\frac{4 a^{5}}{16 (b^{2} b)}$

Multiply $b^{2}$ by $b$ .

Raise $b$ to the power of $1$ .

$\frac{4 a^{5}}{16 (b^{2} b^{1})}$

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

$\frac{4 a^{5}}{16 b^{2 + 1}}$

Add $2$ and $1$ .

$\frac{4 a^{5}}{16 b^{3}}$

Step 3

Cancel the common factor of $4$ and $16$ .

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

$\frac{4 (a^{5})}{16 b^{3}}$

Cancel the common factors.

Factor $4$ out of $16 b^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{a^{5}}{4 b^{3}}$