Basic Math Examples

${(\frac{7 a b}{2 b^{2}})}^{2}$

Step 1

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

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Step 1.1

Factor $b$ out of $7 a b$ .

${(\frac{b (7 a)}{2 b^{2}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

${(\frac{b (7 a)}{b (2 b)})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{b (7 a)}{b (2 b)})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{7 a}{2 b})}^{2}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{7 a}{2 b}$ .

$\frac{{(7 a)}^{2}}{{(2 b)}^{2}}$

Step 2.2

Apply the product rule to $7 a$ .

$\frac{7^{2} a^{2}}{{(2 b)}^{2}}$

Step 2.3

Apply the product rule to $2 b$ .

$\frac{7^{2} a^{2}}{2^{2} b^{2}}$

Step 3

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

$\frac{49 a^{2}}{2^{2} b^{2}}$

Step 4

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

$\frac{49 a^{2}}{4 b^{2}}$