Simplify ((7r^5k)/(4r^2k^3))^2

${(\frac{7 r^{5} k}{4 r^{2} k^{3}})}^{2}$

Step 1

Cancel the common factor of $r^{5}$ and $r^{2}$ .

Factor $r^{2}$ out of $7 r^{5} k$ .

${(\frac{r^{2} (7 r^{3} k)}{4 r^{2} k^{3}})}^{2}$

Cancel the common factors.

Factor $r^{2}$ out of $4 r^{2} k^{3}$ .

${(\frac{r^{2} (7 r^{3} k)}{r^{2} (4 k^{3})})}^{2}$

Cancel the common factor.

${(\frac{r^{2} (7 r^{3} k)}{r^{2} (4 k^{3})})}^{2}$

Rewrite the expression.

${(\frac{7 r^{3} k}{4 k^{3}})}^{2}$

Step 2

Cancel the common factor of $k$ and $k^{3}$ .

Factor $k$ out of $7 r^{3} k$ .

${(\frac{k (7 r^{3})}{4 k^{3}})}^{2}$

Cancel the common factors.

Factor $k$ out of $4 k^{3}$ .

${(\frac{k (7 r^{3})}{k (4 k^{2})})}^{2}$

Cancel the common factor.

${(\frac{k (7 r^{3})}{k (4 k^{2})})}^{2}$

Rewrite the expression.

${(\frac{7 r^{3}}{4 k^{2}})}^{2}$

Step 3

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

Apply the product rule to $\frac{7 r^{3}}{4 k^{2}}$ .

$\frac{{(7 r^{3})}^{2}}{{(4 k^{2})}^{2}}$

Apply the product rule to $7 r^{3}$ .

$\frac{7^{2} {(r^{3})}^{2}}{{(4 k^{2})}^{2}}$

Apply the product rule to $4 k^{2}$ .

$\frac{7^{2} {(r^{3})}^{2}}{4^{2} {(k^{2})}^{2}}$

Step 4

Simplify the numerator.

Raise $7$ to the power of $2$ .

$\frac{49 {(r^{3})}^{2}}{4^{2} {(k^{2})}^{2}}$

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

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

$\frac{49 r^{3 \cdot 2}}{4^{2} {(k^{2})}^{2}}$

Multiply $3$ by $2$ .

$\frac{49 r^{6}}{4^{2} {(k^{2})}^{2}}$

Step 5

Simplify the denominator.

Raise $4$ to the power of $2$ .

$\frac{49 r^{6}}{16 {(k^{2})}^{2}}$

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

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

$\frac{49 r^{6}}{16 k^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{49 r^{6}}{16 k^{4}}$

Simplify ((7r^5k)/(4r^2k^3))^2

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