Algebra Examples

$\sqrt{- 7} \cdot \sqrt{- 7}$

Step 1

Rewrite $- 7$ as $- 1 (7)$ .

$\sqrt{- 1 (7)} \cdot \sqrt{- 7}$

Step 2

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$\sqrt{- 1} \cdot \sqrt{7} \cdot \sqrt{- 7}$

Step 3

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

$i \cdot \sqrt{7} \cdot \sqrt{- 7}$

Step 4

Rewrite $- 7$ as $- 1 (7)$ .

$i \cdot \sqrt{7} \cdot \sqrt{- 1 (7)}$

Step 5

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$i \cdot \sqrt{7} \cdot (\sqrt{- 1} \cdot \sqrt{7})$

Step 6

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

$i \cdot \sqrt{7} \cdot (i \cdot \sqrt{7})$

Step 7

Multiply $i \sqrt{7} (i \sqrt{7})$ .

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Step 7.1

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

$i^{1} i \sqrt{7} \sqrt{7}$

Step 7.2

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

$i^{1} i^{1} \sqrt{7} \sqrt{7}$

Step 7.3

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

$i^{1 + 1} \sqrt{7} \sqrt{7}$

Step 7.4

Add $1$ and $1$ .

$i^{2} \sqrt{7} \sqrt{7}$

Step 7.5

Raise $\sqrt{7}$ to the power of $1$ .

$i^{2} ({\sqrt{7}}^{1} \sqrt{7})$

Step 7.6

Raise $\sqrt{7}$ to the power of $1$ .

$i^{2} ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

Step 7.7

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

$i^{2} {\sqrt{7}}^{1 + 1}$

Step 7.8

Add $1$ and $1$ .

$i^{2} {\sqrt{7}}^{2}$

Step 8

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

$- 1 {\sqrt{7}}^{2}$

Step 9

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 9.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$- 1 {(7^{\frac{1}{2}})}^{2}$

Step 9.2

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

$- 1 \cdot 7^{\frac{1}{2} \cdot 2}$

Step 9.3

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

$- 1 \cdot 7^{\frac{2}{2}}$

Step 9.4

Cancel the common factor of $2$ .

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Step 9.4.1

Cancel the common factor.

$- 1 \cdot 7^{\frac{2}{2}}$

Step 9.4.2

Rewrite the expression.

$- 1 \cdot 7^{1}$

Step 9.5

Evaluate the exponent.

$- 1 \cdot 7$

Step 10

Multiply $- 1$ by $7$ .

$- 7$