Finite Math Examples

$8 \sqrt[4]{24 x^{2} y^{3}} (8 \sqrt[4]{24 x^{2} y^{3}})$

Step 1

Multiply $8 \sqrt[4]{24 x^{2} y^{3}} (8 \sqrt[4]{24 x^{2} y^{3}})$ .

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Step 1.1

Multiply $8$ by $8$ .

$64 \sqrt[4]{24 x^{2} y^{3}} \sqrt[4]{24 x^{2} y^{3}}$

Step 1.2

Raise $\sqrt[4]{24 x^{2} y^{3}}$ to the power of $1$ .

$64 ({\sqrt[4]{24 x^{2} y^{3}}}^{1} \sqrt[4]{24 x^{2} y^{3}})$

Step 1.3

Raise $\sqrt[4]{24 x^{2} y^{3}}$ to the power of $1$ .

$64 ({\sqrt[4]{24 x^{2} y^{3}}}^{1} {\sqrt[4]{24 x^{2} y^{3}}}^{1})$

Step 1.4

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

$64 {\sqrt[4]{24 x^{2} y^{3}}}^{1 + 1}$

Step 1.5

Add $1$ and $1$ .

$64 {\sqrt[4]{24 x^{2} y^{3}}}^{2}$

Step 2

Rewrite ${\sqrt[4]{24 x^{2} y^{3}}}^{2}$ as $\sqrt{24 x^{2} y^{3}}$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{24 x^{2} y^{3}}$ as ${(24 x^{2} y^{3})}^{\frac{1}{4}}$ .

$64 {({(24 x^{2} y^{3})}^{\frac{1}{4}})}^{2}$

Step 2.2

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

$64 {(24 x^{2} y^{3})}^{\frac{1}{4} \cdot 2}$

Step 2.3

Combine $\frac{1}{4}$ and $2$ .

$64 {(24 x^{2} y^{3})}^{\frac{2}{4}}$

Step 2.4

Cancel the common factor of $2$ and $4$ .

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Step 2.4.1

Factor $2$ out of $2$ .

$64 {(24 x^{2} y^{3})}^{\frac{2 (1)}{4}}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$64 {(24 x^{2} y^{3})}^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 2.4.2.2

Cancel the common factor.

$64 {(24 x^{2} y^{3})}^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 2.4.2.3

Rewrite the expression.

$64 {(24 x^{2} y^{3})}^{\frac{1}{2}}$

Step 2.5

Rewrite ${(24 x^{2} y^{3})}^{\frac{1}{2}}$ as $\sqrt{24 x^{2} y^{3}}$ .

$64 \sqrt{24 x^{2} y^{3}}$

Step 3

Rewrite $24 x^{2} y^{3}$ as ${(2 x y)}^{2} \cdot (6 y)$ .

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Step 3.1

Factor $4$ out of $24$ .

$64 \sqrt{4 (6) x^{2} y^{3}}$

Step 3.2

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

$64 \sqrt{2^{2} \cdot 6 x^{2} y^{3}}$

Step 3.3

Factor out $y^{2}$ .

$64 \sqrt{2^{2} \cdot 6 x^{2} (y^{2} y)}$

Step 3.4

Move $6$ .

$64 \sqrt{2^{2} x^{2} y^{2} \cdot 6 y}$

Step 3.5

Rewrite $2^{2} x^{2} y^{2}$ as ${(2 x y)}^{2}$ .

$64 \sqrt{{(2 x y)}^{2} \cdot 6 y}$

Step 3.6

Add parentheses.

$64 \sqrt{{(2 x y)}^{2} \cdot (6 y)}$

Step 4

Pull terms out from under the radical.

$64 (2 x y \sqrt{6 y})$

Step 5

Multiply $2$ by $64$ .

$128 x y \sqrt{6 y}$