Simplify (27p^6)^(5/3)

${(27 p^{6})}^{\frac{5}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $27 p^{6}$ .

$27^{\frac{5}{3}} {(p^{6})}^{\frac{5}{3}}$

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{5}{3}} {(p^{6})}^{\frac{5}{3}}$

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

$3^{3 (\frac{5}{3})} {(p^{6})}^{\frac{5}{3}}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{5}{3})} {(p^{6})}^{\frac{5}{3}}$

Rewrite the expression.

$3^{5} {(p^{6})}^{\frac{5}{3}}$

Step 3

Simplify the expression.

Raise $3$ to the power of $5$ .

$243 {(p^{6})}^{\frac{5}{3}}$

Multiply the exponents in ${(p^{6})}^{\frac{5}{3}}$ .

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

$243 p^{6 (\frac{5}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$243 p^{3 (2) \frac{5}{3}}$

Cancel the common factor.

$243 p^{3 \cdot 2 \frac{5}{3}}$

Rewrite the expression.

$243 p^{2 \cdot 5}$

Multiply $2$ by $5$ .

$243 p^{10}$