Algebra Examples

${(\sqrt{- 75})}^{3}$

Step 1

Rewrite $- 75$ as $- 1 (75)$ .

${\sqrt{- 1 (75)}}^{3}$

Step 2

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

${(\sqrt{- 1} \cdot \sqrt{75})}^{3}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

${(i \cdot \sqrt{75})}^{3}$

Step 4

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 4.1

Factor $25$ out of $75$ .

${(i \cdot \sqrt{25 (3)})}^{3}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

${(i \cdot \sqrt{5^{2} \cdot 3})}^{3}$

${(i \cdot \sqrt{5^{2} \cdot 3})}^{3}$

Step 5

Pull terms out from under the radical.

${(i \cdot (5 \sqrt{3}))}^{3}$

Step 6

Move $5$ to the left of $i$ .

${(5 \cdot i \sqrt{3})}^{3}$

Step 7

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

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Step 7.1

Apply the product rule to $5 i \sqrt{3}$ .

${(5 i)}^{3} {\sqrt{3}}^{3}$

Step 7.2

Apply the product rule to $5 i$ .

$5^{3} i^{3} {\sqrt{3}}^{3}$

$5^{3} i^{3} {\sqrt{3}}^{3}$

Step 8

Raise $5$ to the power of $3$ .

$125 i^{3} {\sqrt{3}}^{3}$

Step 9

Factor out $i^{2}$ .

$125 (i^{2} \cdot i) {\sqrt{3}}^{3}$

Step 10

Rewrite $i^{2}$ as $- 1$ .

$125 (- 1 \cdot i) {\sqrt{3}}^{3}$

Step 11

Rewrite $- 1 i$ as $- i$ .

$125 (- i) {\sqrt{3}}^{3}$

Step 12

Multiply $- 1$ by $125$ .

$- 125 i {\sqrt{3}}^{3}$

Step 13

Rewrite ${\sqrt{3}}^{3}$ as $\sqrt{3^{3}}$ .

$- 125 i \sqrt{3^{3}}$

Step 14

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

$- 125 i \sqrt{27}$

Step 15

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 15.1

Factor $9$ out of $27$ .

$- 125 i \sqrt{9 (3)}$

Step 15.2

Rewrite $9$ as $3^{2}$ .

$- 125 i \sqrt{3^{2} \cdot 3}$

$- 125 i \sqrt{3^{2} \cdot 3}$

Step 16

Pull terms out from under the radical.

$- 125 i (3 \sqrt{3})$

Step 17

Multiply $3$ by $- 125$ .

$- 375 i \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$