Basic Math Examples

${(5 a b)}^{2} \div 25 a^{2} b$

Step 1

Rewrite the division as a fraction.

$\frac{{(5 a b)}^{2}}{25 a^{2} b}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $5 a b$ .

$\frac{{(5 a)}^{2} b^{2}}{25 a^{2} b}$

Step 2.2

Apply the product rule to $5 a$ .

$\frac{5^{2} a^{2} b^{2}}{25 a^{2} b}$

Step 2.3

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

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $25$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

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

Step 3.3

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

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Step 3.3.1

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

$\frac{b \cdot b}{b}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

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

$\frac{b \cdot b}{b^{1}}$

Step 3.3.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot b}{b \cdot 1}$

Step 3.3.2.3

Cancel the common factor.

$\frac{b \cdot b}{b \cdot 1}$

Step 3.3.2.4

Rewrite the expression.

$\frac{b}{1}$

Step 3.3.2.5

Divide $b$ by $1$ .

$b$

$b$

$b$

$b$

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