Basic Math Examples

${(\sqrt[5]{g^{60}})}^{\frac{1}{3}} \sqrt[7]{t^{14}}$

Step 1

Rewrite $g^{60}$ as ${(g^{12})}^{5}$ .

${\sqrt[5]{{(g^{12})}^{5}}}^{\frac{1}{3}} \sqrt[7]{t^{14}}$

Step 2

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

${(g^{12})}^{\frac{1}{3}} \sqrt[7]{t^{14}}$

Step 3

Multiply the exponents in ${(g^{12})}^{\frac{1}{3}}$ .

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Step 3.1

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

$g^{12 (\frac{1}{3})} \sqrt[7]{t^{14}}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $12$ .

$g^{3 (4) \frac{1}{3}} \sqrt[7]{t^{14}}$

Step 3.2.2

Cancel the common factor.

$g^{3 \cdot 4 \frac{1}{3}} \sqrt[7]{t^{14}}$

Step 3.2.3

Rewrite the expression.

$g^{4} \sqrt[7]{t^{14}}$

Step 4

Rewrite $t^{14}$ as ${(t^{2})}^{7}$ .

$g^{4} \sqrt[7]{{(t^{2})}^{7}}$

Step 5

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

$g^{4} t^{2}$