Simplify (x^2)^5(16x^10)^(1/2)

${(x^{2})}^{5} {(16 x^{10})}^{\frac{1}{2}}$

Simplify the expression.

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

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

$x^{2 \cdot 5} {(16 x^{10})}^{\frac{1}{2}}$

Multiply $2$ by $5$ .

$x^{10} {(16 x^{10})}^{\frac{1}{2}}$

Apply the product rule to $16 x^{10}$ .

$x^{10} (16^{\frac{1}{2}} {(x^{10})}^{\frac{1}{2}})$

Rewrite using the commutative property of multiplication.

$16^{\frac{1}{2}} x^{10} {(x^{10})}^{\frac{1}{2}}$

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

${(4^{2})}^{\frac{1}{2}} x^{10} {(x^{10})}^{\frac{1}{2}}$

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

$4^{2 (\frac{1}{2})} x^{10} {(x^{10})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4^{2 (\frac{1}{2})} x^{10} {(x^{10})}^{\frac{1}{2}}$

Rewrite the expression.

$4^{1} x^{10} {(x^{10})}^{\frac{1}{2}}$

Simplify the expression.

Evaluate the exponent.

$4 x^{10} {(x^{10})}^{\frac{1}{2}}$

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

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

$4 x^{10} x^{10 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$4 x^{10} x^{2 (5) \frac{1}{2}}$

Cancel the common factor.

$4 x^{10} x^{2 \cdot 5 \frac{1}{2}}$

Rewrite the expression.

$4 x^{10} x^{5}$

Multiply $x^{10}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$4 (x^{5} x^{10})$

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

$4 x^{5 + 10}$

Add $5$ and $10$ .

$4 x^{15}$