Find the Product -6(2/3p^8)^3

$- 6 {(\frac{2}{3} p^{8})}^{3}$

Step 1

Combine $\frac{2}{3}$ and $p^{8}$ .

$- 6 {(\frac{2 p^{8}}{3})}^{3}$

Step 2

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

Apply the product rule to $\frac{2 p^{8}}{3}$ .

$- 6 \frac{{(2 p^{8})}^{3}}{3^{3}}$

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

$- 6 \frac{2^{3} {(p^{8})}^{3}}{3^{3}}$

Step 3

Simplify the numerator.

Raise $2$ to the power of $3$ .

$- 6 \frac{8 {(p^{8})}^{3}}{3^{3}}$

Multiply the exponents in ${(p^{8})}^{3}$ .

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

$- 6 \frac{8 p^{8 \cdot 3}}{3^{3}}$

Multiply $8$ by $3$ .

$- 6 \frac{8 p^{24}}{3^{3}}$

Step 4

Simplify terms.

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

$- 6 \frac{8 p^{24}}{27}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$3 (- 2) \frac{8 p^{24}}{27}$

Factor $3$ out of $27$ .

$3 \cdot - 2 \frac{8 p^{24}}{3 \cdot 9}$

Cancel the common factor.

$3 \cdot - 2 \frac{8 p^{24}}{3 \cdot 9}$

Rewrite the expression.

$- 2 \frac{8 p^{24}}{9}$

Combine $- 2$ and $\frac{8 p^{24}}{9}$ .

$\frac{- 2 (8 p^{24})}{9}$

Simplify the expression.

Multiply $8$ by $- 2$ .

$\frac{- 16 p^{24}}{9}$

Move the negative in front of the fraction.

$- \frac{16 p^{24}}{9}$