Algebra Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $2$ and $\frac{1}{x^{2}}$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Combine.

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

Step 5

Simplify the expression.

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Step 5.1

Multiply $2$ by $1$ .

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

Step 5.2

Move $3$ to the left of $x^{2}$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Apply the product rule to $3 x$ .

$\frac{2}{3 x^{2}} \cdot \frac{3^{2} x^{2}}{4^{2}}$

Step 7

Simplify terms.

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Step 7.1

Combine.

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

Step 7.2

Cancel the common factor of $3^{2}$ and $3$ .

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Step 7.2.1

Factor $3$ out of $2 (3^{2} x^{2})$ .

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

Step 7.2.2

Cancel the common factors.

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Step 7.2.2.1

Factor $3$ out of $3 x^{2} \cdot 4^{2}$ .

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

Step 7.2.2.2

Cancel the common factor.

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

Step 7.2.2.3

Rewrite the expression.

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

Step 7.3

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

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Step 7.3.1

Cancel the common factor.

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

Step 7.3.2

Rewrite the expression.

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

Step 8

Multiply $2$ by $3$ .

$\frac{6}{4^{2}}$

Step 9

Reduce the expression by cancelling the common factors.

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Step 9.1

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

$\frac{6}{16}$

Step 9.2

Cancel the common factor of $6$ and $16$ .

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Step 9.2.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{16}$

Step 9.2.2

Cancel the common factors.

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Step 9.2.2.1

Factor $2$ out of $16$ .

$\frac{2 \cdot 3}{2 \cdot 8}$

Step 9.2.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 8}$

Step 9.2.2.3

Rewrite the expression.

$\frac{3}{8}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$