Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{3}{2}$ .

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

Step 1.1.2

Apply the product rule to $\frac{3}{2}$ .

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

Step 1.2

Raise $- 1$ to the power of $2$ .

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

Step 1.3

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

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

Step 1.4

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

$4 \frac{9}{2^{2}} - 3$

Step 1.5

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

$4 (\frac{9}{4}) - 3$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Cancel the common factor.

$4 (\frac{9}{4}) - 3$

Step 1.6.2

Rewrite the expression.

$9 - 3$

Step 2

Subtract $3$ from $9$ .

$6$