Simplify cube root of 7x^7* cube root of 9x^4

$\sqrt[3]{7 x^{7}} \cdot \sqrt[3]{9 x^{4}}$

Step 1

Rewrite $7 x^{7}$ as ${(x^{2})}^{3} \cdot (7 x)$ .

Factor out $x^{6}$ .

$\sqrt[3]{7 (x^{6} x)} \cdot \sqrt[3]{9 x^{4}}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$\sqrt[3]{7 ({(x^{2})}^{3} x)} \cdot \sqrt[3]{9 x^{4}}$

Reorder $7$ and ${(x^{2})}^{3}$ .

$\sqrt[3]{{(x^{2})}^{3} \cdot 7 x} \cdot \sqrt[3]{9 x^{4}}$

Add parentheses.

$\sqrt[3]{{(x^{2})}^{3} \cdot (7 x)} \cdot \sqrt[3]{9 x^{4}}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{9 x^{4}}$

Step 3

Rewrite $9 x^{4}$ as $x^{3} \cdot (9 x)$ .

Factor out $x^{3}$ .

$x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{9 (x^{3} x)}$

Reorder $9$ and $x^{3}$ .

$x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{x^{3} \cdot 9 x}$

Add parentheses.

$x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{x^{3} \cdot (9 x)}$

Step 4

Pull terms out from under the radical.

$x^{2} \sqrt[3]{7 x} \cdot (x \sqrt[3]{9 x})$

Step 5

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

Move $x$ .

$x \cdot x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{9 x}$

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

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

$x^{1} x^{2} \sqrt[3]{7 x} \cdot \sqrt[3]{9 x}$

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

$x^{1 + 2} \sqrt[3]{7 x} \cdot \sqrt[3]{9 x}$

Add $1$ and $2$ .

$x^{3} \sqrt[3]{7 x} \cdot \sqrt[3]{9 x}$

Step 6

Multiply $x^{3} \sqrt[3]{7 x} \sqrt[3]{9 x}$ .

Combine using the product rule for radicals.

$x^{3} \sqrt[3]{9 x (7 x)}$

Multiply $7$ by $9$ .

$x^{3} \sqrt[3]{63 x \cdot x}$

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

$x^{3} \sqrt[3]{63 (x^{1} x)}$

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

$x^{3} \sqrt[3]{63 (x^{1} x^{1})}$

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

$x^{3} \sqrt[3]{63 x^{1 + 1}}$

Add $1$ and $1$ .

$x^{3} \sqrt[3]{63 x^{2}}$

Simplify cube root of 7x^7* cube root of 9x^4

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