Algebra Examples

${(\frac{y \frac{1}{4}}{y \frac{3}{2}})}^{2}$

Step 1

Cancel the common factor of $y$ .

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Step 1.1

Cancel the common factor.

${(\frac{y \frac{1}{4}}{y \frac{3}{2}})}^{2}$

Step 1.2

Rewrite the expression.

${(\frac{\frac{1}{4}}{\frac{3}{2}})}^{2}$

${(\frac{\frac{1}{4}}{\frac{3}{2}})}^{2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

${(\frac{1}{4} \cdot \frac{2}{3})}^{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $4$ .

${(\frac{1}{2 (2)} \cdot \frac{2}{3})}^{2}$

Step 3.2

Cancel the common factor.

${(\frac{1}{2 \cdot 2} \cdot \frac{2}{3})}^{2}$

Step 3.3

Rewrite the expression.

${(\frac{1}{2} \cdot \frac{1}{3})}^{2}$

${(\frac{1}{2} \cdot \frac{1}{3})}^{2}$

Step 4

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

${(\frac{1}{2 \cdot 3})}^{2}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $2$ by $3$ .

${(\frac{1}{6})}^{2}$

Step 5.2

Apply the product rule to $\frac{1}{6}$ .

$\frac{1^{2}}{6^{2}}$

Step 5.3

One to any power is one.

$\frac{1}{6^{2}}$

Step 5.4

Raise $6$ to the power of $2$ .

$\frac{1}{36}$

$\frac{1}{36}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{36}$

Decimal Form:

$0.02\overline{7}$

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