Simplify cube root of 5x^(k+1)* cube root of 25x^k

$\sqrt[3]{5 x^{k + 1}} \cdot \sqrt[3]{25 x^{k}}$

Multiply $\sqrt[3]{5 x^{k + 1}} \sqrt[3]{25 x^{k}}$ .

Combine using the product rule for radicals.

$\sqrt[3]{5 x^{k + 1} (25 x^{k})}$

Multiply $25$ by $5$ .

$\sqrt[3]{125 x^{k + 1} x^{k}}$

Multiply $x^{k + 1}$ by $x^{k}$ by adding the exponents.

Move $x^{k}$ .

$\sqrt[3]{125 (x^{k} x^{k + 1})}$

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

$\sqrt[3]{125 x^{k + k + 1}}$

Add $k$ and $k$ .

$\sqrt[3]{125 x^{2 k + 1}}$

Rewrite $125 x^{2 k + 1}$ as $5^{3} x^{2 k + 1^{3}}$ .

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} x^{2 k + 1}}$

Rewrite $1$ as $1^{3}$ .

$\sqrt[3]{5^{3} x^{2 k + 1^{3}}}$

Pull terms out from under the radical.

$5 \sqrt[3]{x^{2 k + 1^{3}}}$

One to any power is one.

$5 \sqrt[3]{x^{2 k + 1}}$