Simplify ((2a^2b^3c^2)/(a^3bc^3))^2

${(\frac{2 a^{2} b^{3} c^{2}}{a^{3} b c^{3}})}^{2}$

Step 1

Cancel the common factor of $a^{2}$ and $a^{3}$ .

Factor $a^{2}$ out of $2 a^{2} b^{3} c^{2}$ .

${(\frac{a^{2} (2 b^{3} c^{2})}{a^{3} b c^{3}})}^{2}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{3} b c^{3}$ .

${(\frac{a^{2} (2 b^{3} c^{2})}{a^{2} (a b c^{3})})}^{2}$

Cancel the common factor.

${(\frac{a^{2} (2 b^{3} c^{2})}{a^{2} (a b c^{3})})}^{2}$

Rewrite the expression.

${(\frac{2 b^{3} c^{2}}{a b c^{3}})}^{2}$

Step 2

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

Factor $b$ out of $2 b^{3} c^{2}$ .

${(\frac{b (2 b^{2} c^{2})}{a b c^{3}})}^{2}$

Cancel the common factors.

Factor $b$ out of $a b c^{3}$ .

${(\frac{b (2 b^{2} c^{2})}{b (a c^{3})})}^{2}$

Cancel the common factor.

${(\frac{b (2 b^{2} c^{2})}{b (a c^{3})})}^{2}$

Rewrite the expression.

${(\frac{2 b^{2} c^{2}}{a c^{3}})}^{2}$

Step 3

Cancel the common factor of $c^{2}$ and $c^{3}$ .

Factor $c^{2}$ out of $2 b^{2} c^{2}$ .

${(\frac{c^{2} (2 b^{2})}{a c^{3}})}^{2}$

Cancel the common factors.

Factor $c^{2}$ out of $a c^{3}$ .

${(\frac{c^{2} (2 b^{2})}{c^{2} (a c)})}^{2}$

Cancel the common factor.

${(\frac{c^{2} (2 b^{2})}{c^{2} (a c)})}^{2}$

Rewrite the expression.

${(\frac{2 b^{2}}{a c})}^{2}$

Step 4

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

Apply the product rule to $\frac{2 b^{2}}{a c}$ .

$\frac{{(2 b^{2})}^{2}}{{(a c)}^{2}}$

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

$\frac{2^{2} {(b^{2})}^{2}}{{(a c)}^{2}}$

Apply the product rule to $a c$ .

$\frac{2^{2} {(b^{2})}^{2}}{a^{2} c^{2}}$

Step 5

Simplify the numerator.

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

$\frac{4 {(b^{2})}^{2}}{a^{2} c^{2}}$

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

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

$\frac{4 b^{2 \cdot 2}}{a^{2} c^{2}}$

Multiply $2$ by $2$ .

$\frac{4 b^{4}}{a^{2} c^{2}}$

Simplify ((2a^2b^3c^2)/(a^3bc^3))^2

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