Algebra Examples

$\sqrt{{(r^{4} g^{6} p^{2})}^{3}}$

Step 1

Apply basic rules of exponents.

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Step 1.1

Apply the product rule to $r^{4} g^{6} p^{2}$ .

$\sqrt{{(r^{4} g^{6})}^{3} {(p^{2})}^{3}}$

Step 1.2

Apply the product rule to $r^{4} g^{6}$ .

$\sqrt{{(r^{4})}^{3} {(g^{6})}^{3} {(p^{2})}^{3}}$

Step 1.3

Multiply the exponents in ${(r^{4})}^{3}$ .

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Step 1.3.1

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

$\sqrt{r^{4 \cdot 3} {(g^{6})}^{3} {(p^{2})}^{3}}$

Step 1.3.2

Multiply $4$ by $3$ .

$\sqrt{r^{12} {(g^{6})}^{3} {(p^{2})}^{3}}$

Step 1.4

Multiply the exponents in ${(g^{6})}^{3}$ .

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Step 1.4.1

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

$\sqrt{r^{12} g^{6 \cdot 3} {(p^{2})}^{3}}$

Step 1.4.2

Multiply $6$ by $3$ .

$\sqrt{r^{12} g^{18} {(p^{2})}^{3}}$

Step 1.5

Multiply the exponents in ${(p^{2})}^{3}$ .

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Step 1.5.1

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

$\sqrt{r^{12} g^{18} p^{2 \cdot 3}}$

Step 1.5.2

Multiply $2$ by $3$ .

$\sqrt{r^{12} g^{18} p^{6}}$

Step 2

Rewrite $r^{12} g^{18} p^{6}$ as ${(r^{6} g^{9} p^{3})}^{2}$ .

$\sqrt{{(r^{6} g^{9} p^{3})}^{2}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$r^{6} g^{9} p^{3}$