Evaluate (2^(1/3)*5^(1/2))^4

${(2^{\frac{1}{3}} \cdot 5^{\frac{1}{2}})}^{4}$

Step 1

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

${(2^{\frac{1}{3}})}^{4} \cdot {(5^{\frac{1}{2}})}^{4}$

Step 2

Multiply the exponents in ${(2^{\frac{1}{3}})}^{4}$ .

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

$2^{\frac{1}{3} \cdot 4} \cdot {(5^{\frac{1}{2}})}^{4}$

Combine $\frac{1}{3}$ and $4$ .

$2^{\frac{4}{3}} \cdot {(5^{\frac{1}{2}})}^{4}$

Step 3

Multiply the exponents in ${(5^{\frac{1}{2}})}^{4}$ .

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

$2^{\frac{4}{3}} \cdot 5^{\frac{1}{2} \cdot 4}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2^{\frac{4}{3}} \cdot 5^{\frac{1}{2} \cdot (2 (2))}$

Cancel the common factor.

$2^{\frac{4}{3}} \cdot 5^{\frac{1}{2} \cdot (2 \cdot 2)}$

Rewrite the expression.

$2^{\frac{4}{3}} \cdot 5^{2}$

Step 4

Raise $5$ to the power of $2$ .

$2^{\frac{4}{3}} \cdot 25$

Step 5

Move $25$ to the left of $2^{\frac{4}{3}}$ .

$25 \cdot 2^{\frac{4}{3}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$25 \cdot 2^{\frac{4}{3}}$

Decimal Form:

$62.99605249 \dots$