Simplify ((p^2t^7)/10)^3

${(\frac{p^{2} t^{7}}{10})}^{3}$

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

Apply the product rule to $\frac{p^{2} t^{7}}{10}$ .

$\frac{{(p^{2} t^{7})}^{3}}{10^{3}}$

Apply the product rule to $p^{2} t^{7}$ .

$\frac{{(p^{2})}^{3} {(t^{7})}^{3}}{10^{3}}$

Simplify the numerator.

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

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

$\frac{p^{2 \cdot 3} {(t^{7})}^{3}}{10^{3}}$

Multiply $2$ by $3$ .

$\frac{p^{6} {(t^{7})}^{3}}{10^{3}}$

Multiply the exponents in ${(t^{7})}^{3}$ .

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

$\frac{p^{6} t^{7 \cdot 3}}{10^{3}}$

Multiply $7$ by $3$ .

$\frac{p^{6} t^{21}}{10^{3}}$

Raise $10$ to the power of $3$ .

$\frac{p^{6} t^{21}}{1000}$