Pre-Algebra Examples

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

Step 1

Apply the product rule to $i \sqrt{7}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

$- 1 \cdot 7^{1}$

Step 3.5

Evaluate the exponent.

$- 1 \cdot 7$

Step 4

Multiply $- 1$ by $7$ .

$- 7$