Finite Math Examples

$(1 - 5 i \sqrt{7}) \cdot (3 \sqrt{7})$

Step 1

Apply the distributive property.

$1 (3 \sqrt{7}) - 5 i \sqrt{7} (3 \sqrt{7})$

Step 2

Multiply $3 \sqrt{7}$ by $1$ .

$3 \sqrt{7} - 5 i \sqrt{7} (3 \sqrt{7})$

Step 3

Multiply $- 5 i \sqrt{7} (3 \sqrt{7})$ .

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Step 3.1

Multiply $3$ by $- 5$ .

$3 \sqrt{7} - 15 i \sqrt{7} \sqrt{7}$

Step 3.2

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

$3 \sqrt{7} - 15 i ({\sqrt{7}}^{1} \sqrt{7})$

Step 3.3

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

$3 \sqrt{7} - 15 i ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

Step 3.4

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

$3 \sqrt{7} - 15 i {\sqrt{7}}^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$3 \sqrt{7} - 15 i {\sqrt{7}}^{2}$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

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

$3 \sqrt{7} - 15 i {(7^{\frac{1}{2}})}^{2}$

Step 4.1.2

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

$3 \sqrt{7} - 15 i \cdot 7^{\frac{1}{2} \cdot 2}$

Step 4.1.3

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

$3 \sqrt{7} - 15 i \cdot 7^{\frac{2}{2}}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$3 \sqrt{7} - 15 i \cdot 7^{\frac{2}{2}}$

Step 4.1.4.2

Rewrite the expression.

$3 \sqrt{7} - 15 i \cdot 7^{1}$

Step 4.1.5

Evaluate the exponent.

$3 \sqrt{7} - 15 i \cdot 7$

Step 4.2

Multiply $7$ by $- 15$ .

$3 \sqrt{7} - 105 i$