Simplify (x^2)^5(36x^14)^(1/2)

${(x^{2})}^{5} {(36 x^{14})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(x^{2})}^{5}$ .

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

$x^{2 \cdot 5} {(36 x^{14})}^{\frac{1}{2}}$

Multiply $2$ by $5$ .

$x^{10} {(36 x^{14})}^{\frac{1}{2}}$

Apply the product rule to $36 x^{14}$ .

$x^{10} (36^{\frac{1}{2}} {(x^{14})}^{\frac{1}{2}})$

Rewrite using the commutative property of multiplication.

$36^{\frac{1}{2}} x^{10} {(x^{14})}^{\frac{1}{2}}$

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

${(6^{2})}^{\frac{1}{2}} x^{10} {(x^{14})}^{\frac{1}{2}}$

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

$6^{2 (\frac{1}{2})} x^{10} {(x^{14})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$6^{2 (\frac{1}{2})} x^{10} {(x^{14})}^{\frac{1}{2}}$

Rewrite the expression.

$6^{1} x^{10} {(x^{14})}^{\frac{1}{2}}$

Step 3

Simplify the expression.

Evaluate the exponent.

$6 x^{10} {(x^{14})}^{\frac{1}{2}}$

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

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

$6 x^{10} x^{14 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$6 x^{10} x^{2 (7) \frac{1}{2}}$

Cancel the common factor.

$6 x^{10} x^{2 \cdot 7 \frac{1}{2}}$

Rewrite the expression.

$6 x^{10} x^{7}$

Step 4

Multiply $x^{10}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$6 (x^{7} x^{10})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 x^{7 + 10}$

Add $7$ and $10$ .

$6 x^{17}$