Trigonometry Examples

$16 \sqrt{33} \cdot (16 \sqrt{33})$

Step 1

Multiply $16 \sqrt{33} (16 \sqrt{33})$ .

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Step 1.1

Multiply $16$ by $16$ .

$256 \sqrt{33} \sqrt{33}$

Step 1.2

Raise $\sqrt{33}$ to the power of $1$ .

$256 ({\sqrt{33}}^{1} \sqrt{33})$

Step 1.3

Raise $\sqrt{33}$ to the power of $1$ .

$256 ({\sqrt{33}}^{1} {\sqrt{33}}^{1})$

Step 1.4

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

$256 {\sqrt{33}}^{1 + 1}$

Step 1.5

Add $1$ and $1$ .

$256 {\sqrt{33}}^{2}$

Step 2

Rewrite ${\sqrt{33}}^{2}$ as $33$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{33}$ as $33^{\frac{1}{2}}$ .

$256 {(33^{\frac{1}{2}})}^{2}$

Step 2.2

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

$256 \cdot 33^{\frac{1}{2} \cdot 2}$

Step 2.3

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

$256 \cdot 33^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$256 \cdot 33^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$256 \cdot 33^{1}$

Step 2.5

Evaluate the exponent.

$256 \cdot 33$

Step 3

Multiply $256$ by $33$ .

$8448$