Algebra Examples

${(144 k^{2} r^{14})}^{\frac{1}{2}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $144 k^{2} r^{14}$ .

${(144 k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 1.2

Apply the product rule to $144 k^{2}$ .

$144^{\frac{1}{2}} {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 2

Rewrite $144$ as $12^{2}$ .

${(12^{2})}^{\frac{1}{2}} {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 3

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

$12^{2 (\frac{1}{2})} {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$12^{2 (\frac{1}{2})} {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 4.2

Rewrite the expression.

$12^{1} {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 5

Evaluate the exponent.

$12 {(k^{2})}^{\frac{1}{2}} {(r^{14})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(k^{2})}^{\frac{1}{2}}$ .

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Step 6.1

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

$12 k^{2 (\frac{1}{2})} {(r^{14})}^{\frac{1}{2}}$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Cancel the common factor.

$12 k^{2 (\frac{1}{2})} {(r^{14})}^{\frac{1}{2}}$

Step 6.2.2

Rewrite the expression.

$12 k^{1} {(r^{14})}^{\frac{1}{2}}$

Step 7

Simplify.

$12 k {(r^{14})}^{\frac{1}{2}}$

Step 8

Multiply the exponents in ${(r^{14})}^{\frac{1}{2}}$ .

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Step 8.1

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

$12 k r^{14 (\frac{1}{2})}$

Step 8.2

Cancel the common factor of $2$ .

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Step 8.2.1

Factor $2$ out of $14$ .

$12 k r^{2 (7) \frac{1}{2}}$

Step 8.2.2

Cancel the common factor.

$12 k r^{2 \cdot 7 \frac{1}{2}}$

Step 8.2.3

Rewrite the expression.

$12 k r^{7}$