Simplify (2/3r^2s^7)^2*(1/6r^3s)

${(\frac{2}{3} r^{2} s^{7})}^{2} \cdot (\frac{1}{6} r^{3} s)$

Rewrite using the commutative property of multiplication.

$\frac{1}{6} {(\frac{2}{3} \cdot r^{2} s^{7})}^{2} r^{3} s$

Combine $\frac{2}{3}$ and $r^{2}$ .

$\frac{1}{6} {(\frac{2 r^{2}}{3} s^{7})}^{2} r^{3} s$

Combine $\frac{2 r^{2}}{3}$ and $s^{7}$ .

$\frac{1}{6} {(\frac{2 r^{2} s^{7}}{3})}^{2} r^{3} s$

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

Apply the product rule to $\frac{2 r^{2} s^{7}}{3}$ .

$\frac{1}{6} \cdot \frac{{(2 r^{2} s^{7})}^{2}}{3^{2}} r^{3} s$

Apply the product rule to $2 r^{2} s^{7}$ .

$\frac{1}{6} \cdot \frac{{(2 r^{2})}^{2} {(s^{7})}^{2}}{3^{2}} r^{3} s$

Apply the product rule to $2 r^{2}$ .

$\frac{1}{6} \cdot \frac{2^{2} {(r^{2})}^{2} {(s^{7})}^{2}}{3^{2}} r^{3} s$

Combine fractions.

Combine.

$\frac{1 (2^{2} {(r^{2})}^{2} {(s^{7})}^{2})}{6 \cdot 3^{2}} r^{3} s$

Simplify the expression.

Multiply $2^{2}$ by $1$ .

$\frac{2^{2} {(r^{2})}^{2} {(s^{7})}^{2}}{6 \cdot 3^{2}} r^{3} s$

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

$\frac{2^{2} {(r^{2})}^{2} {(s^{7})}^{2}}{6 \cdot 9} r^{3} s$

Simplify the numerator.

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

$\frac{4 {(r^{2})}^{2} {(s^{7})}^{2}}{6 \cdot 9} r^{3} s$

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

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

$\frac{4 r^{2 \cdot 2} {(s^{7})}^{2}}{6 \cdot 9} r^{3} s$

Multiply $2$ by $2$ .

$\frac{4 r^{4} {(s^{7})}^{2}}{6 \cdot 9} r^{3} s$

Multiply the exponents in ${(s^{7})}^{2}$ .

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

$\frac{4 r^{4} s^{7 \cdot 2}}{6 \cdot 9} r^{3} s$

Multiply $7$ by $2$ .

$\frac{4 r^{4} s^{14}}{6 \cdot 9} r^{3} s$

Reduce the expression by cancelling the common factors.

Multiply $6$ by $9$ .

$\frac{4 r^{4} s^{14}}{54} r^{3} s$

Cancel the common factor of $4$ and $54$ .

Factor $2$ out of $4 r^{4} s^{14}$ .

$\frac{2 (2 r^{4} s^{14})}{54} r^{3} s$

Cancel the common factors.

Factor $2$ out of $54$ .

$\frac{2 (2 r^{4} s^{14})}{2 (27)} r^{3} s$

Cancel the common factor.

$\frac{2 (2 r^{4} s^{14})}{2 \cdot 27} r^{3} s$

Rewrite the expression.

$\frac{2 r^{4} s^{14}}{27} r^{3} s$

Multiply $\frac{2 r^{4} s^{14}}{27} r^{3}$ .

Combine $\frac{2 r^{4} s^{14}}{27}$ and $r^{3}$ .

$\frac{2 r^{4} s^{14} r^{3}}{27} s$

Multiply $r^{4}$ by $r^{3}$ by adding the exponents.

Move $r^{3}$ .

$\frac{2 (r^{3} r^{4}) s^{14}}{27} s$

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

$\frac{2 r^{3 + 4} s^{14}}{27} s$

Add $3$ and $4$ .

$\frac{2 r^{7} s^{14}}{27} s$

Multiply $\frac{2 r^{7} s^{14}}{27} s$ .

Combine $\frac{2 r^{7} s^{14}}{27}$ and $s$ .

$\frac{2 r^{7} s^{14} s}{27}$

Raise $s$ to the power of $1$ .

$\frac{2 r^{7} (s^{1} s^{14})}{27}$

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

$\frac{2 r^{7} s^{1 + 14}}{27}$

Add $1$ and $14$ .

$\frac{2 r^{7} s^{15}}{27}$

Simplify (2/3r^2s^7)^2*(1/6r^3s)

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