Simplify cube root of b^2 square root of b^9

$\sqrt[3]{b^{2}} \sqrt{b^{9}}$

Step 1

Rewrite $b^{9}$ as ${(b^{4})}^{2} b$ .

Factor out $b^{8}$ .

$\sqrt[3]{b^{2}} \sqrt{b^{8} b}$

Rewrite $b^{8}$ as ${(b^{4})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $\sqrt[3]{b^{2}} (b^{4} \sqrt{b})$ .

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{b^{2}}$ as $b^{\frac{2}{3}}$ .

$b^{4} (b^{\frac{2}{3}} \sqrt{b})$

Rewrite $b^{\frac{2}{3}}$ as $b^{\frac{4}{6}}$ .

$b^{4} (b^{\frac{4}{6}} \sqrt{b})$

Rewrite $b^{\frac{4}{6}}$ as $\sqrt[6]{b^{4}}$ .

$b^{4} (\sqrt[6]{b^{4}} \sqrt{b})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b}$ as $b^{\frac{1}{2}}$ .

$b^{4} (\sqrt[6]{b^{4}} b^{\frac{1}{2}})$

Rewrite $b^{\frac{1}{2}}$ as $b^{\frac{3}{6}}$ .

$b^{4} (\sqrt[6]{b^{4}} b^{\frac{3}{6}})$

Rewrite $b^{\frac{3}{6}}$ as $\sqrt[6]{b^{3}}$ .

$b^{4} (\sqrt[6]{b^{4}} \sqrt[6]{b^{3}})$

Combine using the product rule for radicals.

$b^{4} \sqrt[6]{b^{4} b^{3}}$

Multiply $b^{4}$ by $b^{3}$ by adding the exponents.

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

$b^{4} \sqrt[6]{b^{4 + 3}}$

Add $4$ and $3$ .

$b^{4} \sqrt[6]{b^{7}}$

Step 4

Factor out $b^{6}$ .

$b^{4} \sqrt[6]{b^{6} b}$

Step 5

Pull terms out from under the radical.

$b^{4} (b \sqrt[6]{b})$

Step 6

Multiply $b^{4}$ by $b$ by adding the exponents.

Move $b$ .

$b \cdot b^{4} \sqrt[6]{b}$

Multiply $b$ by $b^{4}$ .

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

$b^{1} b^{4} \sqrt[6]{b}$

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

$b^{1 + 4} \sqrt[6]{b}$

Add $1$ and $4$ .

$b^{5} \sqrt[6]{b}$

Simplify cube root of b^2 square root of b^9

Related Questions

Support LCMGCF.com by disabling your adblocker.