Algebra Examples

$- 4 i \sqrt{- 10} \cdot 5 \sqrt{- 10}$

Step 1

Rewrite $- 10$ as $- 1 (10)$ .

$- 4 i \sqrt{- 1 (10)} \cdot (5 \sqrt{- 10})$

Step 2

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$- 4 i (\sqrt{- 1} \cdot \sqrt{10}) \cdot (5 \sqrt{- 10})$

Step 3

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

$- 4 i (i \cdot \sqrt{10}) \cdot (5 \sqrt{- 10})$

Step 4

Rewrite $- 10$ as $- 1 (10)$ .

$- 4 i (i \cdot \sqrt{10}) \cdot (5 \sqrt{- 1 (10)})$

Step 5

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$- 4 i (i \cdot \sqrt{10}) \cdot (5 (\sqrt{- 1} \cdot \sqrt{10}))$

Step 6

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

$- 4 i (i \cdot \sqrt{10}) \cdot (5 (i \cdot \sqrt{10}))$

Step 7

Multiply $- 4 i (i \sqrt{10})$ .

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Step 7.1

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

$- 4 (i^{1} i) \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 7.2

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

$- 4 (i^{1} i^{1}) \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 7.3

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

$- 4 i^{1 + 1} \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 7.4

Add $1$ and $1$ .

$- 4 i^{2} \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 8

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

$- 4 \cdot - 1 \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 9

Multiply $- 4$ by $- 1$ .

$4 \sqrt{10} \cdot (5 (i \cdot \sqrt{10}))$

Step 10

Multiply $4 \sqrt{10} (5 i \sqrt{10})$ .

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Step 10.1

Multiply $5$ by $4$ .

$20 \sqrt{10} (i \sqrt{10})$

Step 10.2

Raise $\sqrt{10}$ to the power of $1$ .

$20 ({\sqrt{10}}^{1} \sqrt{10}) i$

Step 10.3

Raise $\sqrt{10}$ to the power of $1$ .

$20 ({\sqrt{10}}^{1} {\sqrt{10}}^{1}) i$

Step 10.4

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

$20 {\sqrt{10}}^{1 + 1} i$

Step 10.5

Add $1$ and $1$ .

$20 {\sqrt{10}}^{2} i$

Step 11

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 11.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$20 {(10^{\frac{1}{2}})}^{2} i$

Step 11.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$20 \cdot 10^{\frac{1}{2} \cdot 2} i$

Step 11.3

Combine $\frac{1}{2}$ and $2$ .

$20 \cdot 10^{\frac{2}{2}} i$

Step 11.4

Cancel the common factor of $2$ .

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Step 11.4.1

Cancel the common factor.

$20 \cdot 10^{\frac{2}{2}} i$

Step 11.4.2

Rewrite the expression.

$20 \cdot 10^{1} i$

Step 11.5

Evaluate the exponent.

$20 \cdot 10 i$

Step 12

Multiply $20$ by $10$ .

$200 i$