Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $- 3 \cdot 3^{\frac{1}{2}}$ .

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Step 1.1.1

Factor out negative.

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

Step 1.1.2

Raise $3$ to the power of $1$ .

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

Step 1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.1.4

Write $1$ as a fraction with a common denominator.

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

Step 1.1.5

Combine the numerators over the common denominator.

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

Step 1.1.6

Add $2$ and $1$ .

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

Step 1.2

Move ${(3)}^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 1.3

Multiply $3$ by $3^{- \frac{1}{2}}$ by adding the exponents.

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Step 1.3.1

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

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Step 1.3.1.1

Raise $3$ to the power of $1$ .

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

Step 1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3^{\frac{3}{2}} + \frac{3^{1 - \frac{1}{2}}}{4}$

Step 1.3.2

Write $1$ as a fraction with a common denominator.

$- 3^{\frac{3}{2}} + \frac{3^{\frac{2}{2} - \frac{1}{2}}}{4}$

Step 1.3.3

Combine the numerators over the common denominator.

$- 3^{\frac{3}{2}} + \frac{3^{\frac{2 - 1}{2}}}{4}$

Step 1.3.4

Subtract $1$ from $2$ .

$- 3^{\frac{3}{2}} + \frac{3^{\frac{1}{2}}}{4}$

Step 2

To write $- 3^{\frac{3}{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3

Combine $- 3^{\frac{3}{2}}$ and $\frac{4}{4}$ .

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

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

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

Step 4.2

Multiply $4$ by $- 1$ .

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

Step 5

Factor $- 1$ out of $- 4 \cdot 3^{\frac{3}{2}}$ .

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

Step 6

Factor $- 1$ out of $3^{\frac{1}{2}}$ .

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

Step 7

Factor $- 1$ out of $- (4 \cdot 3^{\frac{3}{2}}) - 1 (- 3^{\frac{1}{2}})$ .

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

Step 8

Simplify the expression.

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Step 8.1

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

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

Step 8.2

Move the negative in front of the fraction.

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 4.76313972 \dots$