Basic Math Examples

${(\sqrt{13})}^{2} - 4 \cdot 1 \cdot 42$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

${(13^{\frac{1}{2}})}^{2} - 4 \cdot 1 \cdot 42$

Step 1.1.2

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

$13^{\frac{1}{2} \cdot 2} - 4 \cdot 1 \cdot 42$

Step 1.1.3

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

$13^{\frac{2}{2}} - 4 \cdot 1 \cdot 42$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$13^{\frac{2}{2}} - 4 \cdot 1 \cdot 42$

Step 1.1.4.2

Rewrite the expression.

$13^{1} - 4 \cdot 1 \cdot 42$

Step 1.1.5

Evaluate the exponent.

$13 - 4 \cdot 1 \cdot 42$

Step 1.2

Multiply $- 4 \cdot 1 \cdot 42$ .

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Step 1.2.1

Multiply $- 4$ by $1$ .

$13 - 4 \cdot 42$

Step 1.2.2

Multiply $- 4$ by $42$ .

$13 - 168$

Step 2

Subtract $168$ from $13$ .

$- 155$