Algebra Examples

${(\frac{4 a b^{2}}{5 a b})}^{2}$

Step 1

Cancel the common factor of $a$ .

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Step 1.1

Cancel the common factor.

${(\frac{4 a b^{2}}{5 a b})}^{2}$

Step 1.2

Rewrite the expression.

${(\frac{4 b^{2}}{5 b})}^{2}$

${(\frac{4 b^{2}}{5 b})}^{2}$

Step 2

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

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Step 2.1

Factor $b$ out of $4 b^{2}$ .

${(\frac{b (4 b)}{5 b})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $b$ out of $5 b$ .

${(\frac{b (4 b)}{b \cdot 5})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{b (4 b)}{b \cdot 5})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{4 b}{5})}^{2}$

${(\frac{4 b}{5})}^{2}$

${(\frac{4 b}{5})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $\frac{4 b}{5}$ .

$\frac{{(4 b)}^{2}}{5^{2}}$

Step 3.2

Apply the product rule to $4 b$ .

$\frac{4^{2} b^{2}}{5^{2}}$

$\frac{4^{2} b^{2}}{5^{2}}$

Step 4

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

$\frac{16 b^{2}}{5^{2}}$

Step 5

Raise $5$ to the power of $2$ .

$\frac{16 b^{2}}{25}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$