Simplify ((x^2y^13)÷(y^0))^2

${(x^{2} y^{13} \div y^{0})}^{2}$

Rewrite the division as a fraction.

${(\frac{x^{2} y^{13}}{y^{0}})}^{2}$

Move $y^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{2} y^{13} y^{0})}^{2}$

Multiply $y^{13}$ by $y^{0}$ by adding the exponents.

Move $y^{0}$ .

${(x^{2} (y^{0} y^{13}))}^{2}$

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

${(x^{2} y^{0 + 13})}^{2}$

Add $0$ and $13$ .

${(x^{2} y^{13})}^{2}$

Apply the product rule to $x^{2} y^{13}$ .

${(x^{2})}^{2} {(y^{13})}^{2}$

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

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

$x^{2 \cdot 2} {(y^{13})}^{2}$

Multiply $2$ by $2$ .

$x^{4} {(y^{13})}^{2}$

Multiply the exponents in ${(y^{13})}^{2}$ .

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

$x^{4} y^{13 \cdot 2}$

Multiply $13$ by $2$ .

$x^{4} y^{26}$