Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $2$ and $1$ .

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

Step 2

To write $- \frac{1}{2 \cdot 3^{\frac{1}{2}}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

To write $- \frac{3^{\frac{3}{2}}}{4}$ as a fraction with a common denominator, multiply by $\frac{3^{\frac{1}{2}}}{3^{\frac{1}{2}}}$ .

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

Step 4

Write each expression with a common denominator of $4 \cdot 3^{\frac{1}{2}}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $2$ .

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

Step 4.3

Multiply $\frac{3^{\frac{3}{2}}}{4}$ by $\frac{3^{\frac{1}{2}}}{3^{\frac{1}{2}}}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Divide $3$ by $2$ .

$\frac{- 2 - 3^{1.5} \cdot 3^{\frac{1}{2}}}{4 \cdot 3^{\frac{1}{2}}}$

Step 6.2

Raise $3$ to the power of $1.5$ .

$\frac{- 2 - 1 \cdot 5.19615242 \cdot 3^{\frac{1}{2}}}{4 \cdot 3^{\frac{1}{2}}}$

Step 6.3

Multiply $- 1$ by $5.19615242$ .

$\frac{- 2 - 5.19615242 \cdot 3^{\frac{1}{2}}}{4 \cdot 3^{\frac{1}{2}}}$

Step 6.4

Divide $1$ by $2$ .

$\frac{- 2 - 5.19615242 \cdot 3^{0.5}}{4 \cdot 3^{\frac{1}{2}}}$

Step 6.5

Raise $3$ to the power of $0.5$ .

$\frac{- 2 - 5.19615242 \cdot 1.7320508}{4 \cdot 3^{\frac{1}{2}}}$

Step 6.6

Multiply $- 5.19615242$ by $1.7320508$ .

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

Step 6.7

Subtract $9$ from $- 2$ .

$\frac{- 11}{4 \cdot 3^{\frac{1}{2}}}$

Step 7

Move the negative in front of the fraction.

$- \frac{11}{4 \cdot 3^{\frac{1}{2}}}$

Step 8

Divide $1$ by $2$ .

$- \frac{11}{4 \cdot 3^{0.5}}$

Step 9

Raise $3$ to the power of $0.5$ .

$- \frac{11}{4 \cdot 1.7320508}$

Step 10

Multiply $4$ by $1.7320508$ .

$- \frac{11}{6.92820323}$

Step 11

Divide $11$ by $6.92820323$ .

$- 1 \cdot 1.58771324$

Step 12

Multiply $- 1$ by $1.58771324$ .

$- 1.58771324$