Simplify the Radical Expression ((3q^(5/2)r^(1/4))/(6^(1/2)))^2

${(\frac{3 q^{\frac{5}{2}} r^{\frac{1}{4}}}{6^{\frac{1}{2}}})}^{2}$

Step 1

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

Apply the product rule to $\frac{3 q^{\frac{5}{2}} r^{\frac{1}{4}}}{6^{\frac{1}{2}}}$ .

$\frac{{(3 q^{\frac{5}{2}} r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Apply the product rule to $3 q^{\frac{5}{2}} r^{\frac{1}{4}}$ .

$\frac{{(3 q^{\frac{5}{2}})}^{2} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Apply the product rule to $3 q^{\frac{5}{2}}$ .

$\frac{3^{2} {(q^{\frac{5}{2}})}^{2} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Step 2

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 {(q^{\frac{5}{2}})}^{2} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Multiply the exponents in ${(q^{\frac{5}{2}})}^{2}$ .

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

$\frac{9 q^{\frac{5}{2} \cdot 2} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 q^{\frac{5}{2} \cdot 2} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

Rewrite the expression.

$\frac{9 q^{5} {(r^{\frac{1}{4}})}^{2}}{{(6^{\frac{1}{2}})}^{2}}$

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

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

$\frac{9 q^{5} r^{\frac{1}{4} \cdot 2}}{{(6^{\frac{1}{2}})}^{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{9 q^{5} r^{\frac{1}{2 (2)} \cdot 2}}{{(6^{\frac{1}{2}})}^{2}}$

Cancel the common factor.

$\frac{9 q^{5} r^{\frac{1}{2 \cdot 2} \cdot 2}}{{(6^{\frac{1}{2}})}^{2}}$

Rewrite the expression.

$\frac{9 q^{5} r^{\frac{1}{2}}}{{(6^{\frac{1}{2}})}^{2}}$

Step 3

Simplify the denominator.

Multiply the exponents in ${(6^{\frac{1}{2}})}^{2}$ .

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

$\frac{9 q^{5} r^{\frac{1}{2}}}{6^{\frac{1}{2} \cdot 2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 q^{5} r^{\frac{1}{2}}}{6^{\frac{1}{2} \cdot 2}}$

Rewrite the expression.

$\frac{9 q^{5} r^{\frac{1}{2}}}{6^{1}}$

Evaluate the exponent.

$\frac{9 q^{5} r^{\frac{1}{2}}}{6}$

Step 4

Factor $3$ out of $9 q^{5} r^{\frac{1}{2}}$ .

$\frac{3 (3 q^{5} r^{\frac{1}{2}})}{6}$

Step 5

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 (3 q^{5} r^{\frac{1}{2}})}{3 (2)}$

Cancel the common factor.

$\frac{3 (3 q^{5} r^{\frac{1}{2}})}{3 \cdot 2}$

Rewrite the expression.

$\frac{3 q^{5} r^{\frac{1}{2}}}{2}$

Simplify the Radical Expression ((3q^(5/2)r^(1/4))/(6^(1/2)))^2

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