Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

One to any power is one.

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

Step 1.2

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

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

Step 1.3

One to any power is one.

$\frac{2}{3} - 4 \cdot 1$

Step 1.4

Multiply $- 4$ by $1$ .

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

Step 2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Combine $- 4$ and $\frac{3}{3}$ .

$\frac{2}{3} + \frac{- 4 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $3$ .

$\frac{2 - 12}{3}$

Step 5.2

Subtract $12$ from $2$ .

$\frac{- 10}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{10}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{10}{3}$

Decimal Form:

$- 3.\overline{3}$

Mixed Number Form:

$- 3 \frac{1}{3}$