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Simplify (x^2y^8)^2

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

Step 1

Apply the product rule to $x^{2} y^{8}$ .

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

Step 2

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

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

$x^{2 \cdot 2} {(y^{8})}^{2}$

Multiply $2$ by $2$ .

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

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

Step 3

Multiply the exponents in ${(y^{8})}^{2}$ .

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

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

Multiply $8$ by $2$ .

$x^{4} y^{16}$

$x^{4} y^{16}$

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