Simplify (2x^4y^3)^2

${(2 x^{4} y^{3})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 x^{4} y^{3}$ .

${(2 x^{4})}^{2} {(y^{3})}^{2}$

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

$2^{2} {(x^{4})}^{2} {(y^{3})}^{2}$

Step 2

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

$4 {(x^{4})}^{2} {(y^{3})}^{2}$

Step 3

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

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

$4 x^{4 \cdot 2} {(y^{3})}^{2}$

Multiply $4$ by $2$ .

$4 x^{8} {(y^{3})}^{2}$

Step 4

Multiply the exponents in ${(y^{3})}^{2}$ .

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

$4 x^{8} y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$4 x^{8} y^{6}$