Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $3$ .

$\frac{27 - 3^{2}}{{(\frac{3}{4})}^{2}}$

Step 1.2

Raise $3$ to the power of $2$ .

$\frac{27 - 1 \cdot 9}{{(\frac{3}{4})}^{2}}$

Step 1.3

Multiply $- 1$ by $9$ .

$\frac{27 - 9}{{(\frac{3}{4})}^{2}}$

Step 1.4

Subtract $9$ from $27$ .

$\frac{18}{{(\frac{3}{4})}^{2}}$

$\frac{18}{{(\frac{3}{4})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{3}{4}$ .

$\frac{18}{\frac{3^{2}}{4^{2}}}$

Step 2.2

Raise $3$ to the power of $2$ .

$\frac{18}{\frac{9}{4^{2}}}$

Step 2.3

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

$\frac{18}{\frac{9}{16}}$

$\frac{18}{\frac{9}{16}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$18 (\frac{16}{9})$

Step 4

Cancel the common factor of $9$ .

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Step 4.1

Factor $9$ out of $18$ .

$9 (2) \frac{16}{9}$

Step 4.2

Cancel the common factor.

$9 \cdot 2 \frac{16}{9}$

Step 4.3

Rewrite the expression.

$2 \cdot 16$

$2 \cdot 16$

Step 5

Multiply $2$ by $16$ .

$32$

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