Evaluate (36k^4m^10)^(1/2)

${(36 k^{4} m^{10})}^{\frac{1}{2}}$

Step 1

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

Apply the product rule to $36 k^{4} m^{10}$ .

${(36 k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Apply the product rule to $36 k^{4}$ .

$36^{\frac{1}{2}} {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Step 2

Simplify the expression.

Rewrite $36$ as $6^{2}$ .

${(6^{2})}^{\frac{1}{2}} {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

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

$6^{2 (\frac{1}{2})} {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$6^{2 (\frac{1}{2})} {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Rewrite the expression.

$6^{1} {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Step 4

Simplify the expression.

Evaluate the exponent.

$6 {(k^{4})}^{\frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Multiply the exponents in ${(k^{4})}^{\frac{1}{2}}$ .

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

$6 k^{4 (\frac{1}{2})} {(m^{10})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$6 k^{2 (2) \frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Cancel the common factor.

$6 k^{2 \cdot 2 \frac{1}{2}} {(m^{10})}^{\frac{1}{2}}$

Rewrite the expression.

$6 k^{2} {(m^{10})}^{\frac{1}{2}}$

Multiply the exponents in ${(m^{10})}^{\frac{1}{2}}$ .

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

$6 k^{2} m^{10 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$6 k^{2} m^{2 (5) \frac{1}{2}}$

Cancel the common factor.

$6 k^{2} m^{2 \cdot 5 \frac{1}{2}}$

Rewrite the expression.

$6 k^{2} m^{5}$