Evaluate (7x^3)^2(x^8)^(1/2)

${(7 x^{3})}^{2} {(x^{8})}^{\frac{1}{2}}$

Apply the product rule to $7 x^{3}$ .

$7^{2} {(x^{3})}^{2} {(x^{8})}^{\frac{1}{2}}$

Raise $7$ to the power of $2$ .

$49 {(x^{3})}^{2} {(x^{8})}^{\frac{1}{2}}$

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$49 x^{3 \cdot 2} {(x^{8})}^{\frac{1}{2}}$

Multiply $3$ by $2$ .

$49 x^{6} {(x^{8})}^{\frac{1}{2}}$

Multiply the exponents in ${(x^{8})}^{\frac{1}{2}}$ .

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

$49 x^{6} x^{8 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$49 x^{6} x^{2 (4) \frac{1}{2}}$

Cancel the common factor.

$49 x^{6} x^{2 \cdot 4 \frac{1}{2}}$

Rewrite the expression.

$49 x^{6} x^{4}$

Multiply $x^{6}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$49 (x^{4} x^{6})$

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

$49 x^{4 + 6}$

Add $4$ and $6$ .

$49 x^{10}$