Simplify (36e^16f^64)^(1/2)

${(36 e^{16} f^{64})}^{\frac{1}{2}}$

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

Apply the product rule to $36 e^{16} f^{64}$ .

${(36 e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Apply the product rule to $36 e^{16}$ .

$36^{\frac{1}{2}} {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Simplify the expression.

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

${(6^{2})}^{\frac{1}{2}} {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

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

$6^{2 (\frac{1}{2})} {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6^{2 (\frac{1}{2})} {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Rewrite the expression.

$6^{1} {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Simplify the expression.

Evaluate the exponent.

$6 {(e^{16})}^{\frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Multiply the exponents in ${(e^{16})}^{\frac{1}{2}}$ .

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

$6 e^{16 (\frac{1}{2})} {(f^{64})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$6 e^{2 (8) \frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Cancel the common factor.

$6 e^{2 \cdot 8 \frac{1}{2}} {(f^{64})}^{\frac{1}{2}}$

Rewrite the expression.

$6 e^{8} {(f^{64})}^{\frac{1}{2}}$

Multiply the exponents in ${(f^{64})}^{\frac{1}{2}}$ .

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

$6 e^{8} f^{64 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $64$ .

$6 e^{8} f^{2 (32) \frac{1}{2}}$

Cancel the common factor.

$6 e^{8} f^{2 \cdot 32 \frac{1}{2}}$

Rewrite the expression.

$6 e^{8} f^{32}$