Simplify the Radical Expression ((16c^14)/(81d^18))^(1/2)

${(\frac{16 c^{14}}{81 d^{18}})}^{\frac{1}{2}}$

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

Apply the product rule to $\frac{16 c^{14}}{81 d^{18}}$ .

$\frac{{(16 c^{14})}^{\frac{1}{2}}}{{(81 d^{18})}^{\frac{1}{2}}}$

Apply the product rule to $16 c^{14}$ .

$\frac{16^{\frac{1}{2}} {(c^{14})}^{\frac{1}{2}}}{{(81 d^{18})}^{\frac{1}{2}}}$

Apply the product rule to $81 d^{18}$ .

$\frac{16^{\frac{1}{2}} {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{{(4^{2})}^{\frac{1}{2}} {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

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

$\frac{4^{2 (\frac{1}{2})} {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4^{2 (\frac{1}{2})} {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4^{1} {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{4 {(c^{14})}^{\frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

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

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

$\frac{4 c^{14 (\frac{1}{2})}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$\frac{4 c^{2 (7) \frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{4 c^{2 \cdot 7 \frac{1}{2}}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4 c^{7}}{81^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$\frac{4 c^{7}}{{(9^{2})}^{\frac{1}{2}} {(d^{18})}^{\frac{1}{2}}}$

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

$\frac{4 c^{7}}{9^{2 (\frac{1}{2})} {(d^{18})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 c^{7}}{9^{2 (\frac{1}{2})} {(d^{18})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4 c^{7}}{9^{1} {(d^{18})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{4 c^{7}}{9 {(d^{18})}^{\frac{1}{2}}}$

Multiply the exponents in ${(d^{18})}^{\frac{1}{2}}$ .

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

$\frac{4 c^{7}}{9 d^{18 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Factor $2$ out of $18$ .

$\frac{4 c^{7}}{9 d^{2 (9) \frac{1}{2}}}$

Cancel the common factor.

$\frac{4 c^{7}}{9 d^{2 \cdot 9 \frac{1}{2}}}$

Rewrite the expression.

$\frac{4 c^{7}}{9 d^{9}}$

Simplify the Radical Expression ((16c^14)/(81d^18))^(1/2)

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