Simplify 4 cube root of 25x^5* cube root of 5x

$4 \sqrt[3]{25 x^{5}} \cdot \sqrt[3]{5 x}$

Step 1

Rewrite $25 x^{5}$ as $x^{3} \cdot (25 x^{2})$ .

Factor out $x^{3}$ .

$4 \sqrt[3]{25 (x^{3} x^{2})} \cdot \sqrt[3]{5 x}$

Reorder $25$ and $x^{3}$ .

$4 \sqrt[3]{x^{3} \cdot 25 x^{2}} \cdot \sqrt[3]{5 x}$

Add parentheses.

$4 \sqrt[3]{x^{3} \cdot (25 x^{2})} \cdot \sqrt[3]{5 x}$

Step 2

Pull terms out from under the radical.

$4 (x \sqrt[3]{25 x^{2}}) \cdot \sqrt[3]{5 x}$

Step 3

Multiply $4 x \sqrt[3]{25 x^{2}} \sqrt[3]{5 x}$ .

Combine using the product rule for radicals.

$4 x \sqrt[3]{5 x (25 x^{2})}$

Multiply $25$ by $5$ .

$4 x \sqrt[3]{125 x \cdot x^{2}}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$4 x \sqrt[3]{125 (x^{2} x)}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$4 x \sqrt[3]{125 (x^{2} x^{1})}$

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

$4 x \sqrt[3]{125 x^{2 + 1}}$

Add $2$ and $1$ .

$4 x \sqrt[3]{125 x^{3}}$

Step 4

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

$4 x \sqrt[3]{{(5 x)}^{3}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$4 x (5 x)$

Step 6

Rewrite using the commutative property of multiplication.

$4 \cdot 5 x \cdot x$

Step 7

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 \cdot 5 (x \cdot x)$

Multiply $x$ by $x$ .

$4 \cdot 5 x^{2}$

Step 8

Multiply $4$ by $5$ .

$20 x^{2}$

Simplify 4 cube root of 25x^5* cube root of 5x

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