Algebra Examples

$4 \sqrt{2} \cdot (5 \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$4 \sqrt{2} \cdot (5 \sqrt{4 (2)})$

Rewrite $4$ as $2^{2}$ .

$4 \sqrt{2} \cdot (5 \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$4 \sqrt{2} \cdot (5 (2 \sqrt{2}))$

Multiply $2$ by $5$ .

$4 \sqrt{2} \cdot (10 \sqrt{2})$

Multiply $4 \sqrt{2} (10 \sqrt{2})$ .

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Multiply $10$ by $4$ .

$40 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$40 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$40 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$40 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$40 {\sqrt{2}}^{2}$

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

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

$40 {(2^{\frac{1}{2}})}^{2}$

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

$40 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$40 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$40 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$40 \cdot 2^{1}$

Evaluate the exponent.

$40 \cdot 2$

Multiply $40$ by $2$ .

$80$