Simplify ( cube root of 9)÷( square root of 3)

Solve Math

Algebra

$\sqrt[3]{9} \div \sqrt{3}$

Rewrite the division as a fraction.

$\frac{\sqrt[3]{9}}{\sqrt{3}}$

Multiply $\frac{\sqrt[3]{9}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt[3]{9}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Tap for more steps...

Multiply $\frac{\sqrt[3]{9}}{\sqrt{3}}$ and $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt[3]{9} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt[3]{9} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt[3]{9} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$\frac{\sqrt[3]{9} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\sqrt[3]{9} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt[3]{9} \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$\frac{\sqrt[3]{9} \sqrt{3}}{3}$

Simplify the numerator.

Tap for more steps...

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

Tap for more steps...

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$\frac{9^{\frac{1}{3}} \sqrt{3}}{3}$

Rewrite $9^{\frac{1}{3}}$ as $9^{\frac{2}{6}}$ .

$\frac{9^{\frac{2}{6}} \sqrt{3}}{3}$

Rewrite $9^{\frac{2}{6}}$ as $\sqrt[6]{9^{2}}$ .

$\frac{\sqrt[6]{9^{2}} \sqrt{3}}{3}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\sqrt[6]{9^{2}} \cdot 3^{\frac{1}{2}}}{3}$

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

$\frac{\sqrt[6]{9^{2}} \cdot 3^{\frac{3}{6}}}{3}$

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

$\frac{\sqrt[6]{9^{2}} \sqrt[6]{3^{3}}}{3}$

Combine using the product rule for radicals.

$\frac{\sqrt[6]{9^{2} \cdot 3^{3}}}{3}$

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt[6]{{(3^{2})}^{2} \cdot 3^{3}}}{3}$

Multiply the exponents in ${(3^{2})}^{2}$ .

Tap for more steps...

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

$\frac{\sqrt[6]{3^{2 \cdot 2} \cdot 3^{3}}}{3}$

Multiply $2$ by $2$ .

$\frac{\sqrt[6]{3^{4} \cdot 3^{3}}}{3}$

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

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

Add $4$ and $3$ .

$\frac{\sqrt[6]{3^{7}}}{3}$

Simplify the numerator.

Tap for more steps...

Raise $3$ to the power of $7$ .

$\frac{\sqrt[6]{2187}}{3}$

Rewrite $2187$ as $3^{6} \cdot 3$ .

Tap for more steps...

Factor $729$ out of $2187$ .

$\frac{\sqrt[6]{729 (3)}}{3}$

Rewrite $729$ as $3^{6}$ .

$\frac{\sqrt[6]{3^{6} \cdot 3}}{3}$

Pull terms out from under the radical.

$\frac{3 \sqrt[6]{3}}{3}$

Cancel the common factor of $3$ .

Tap for more steps...

Cancel the common factor.

$\frac{3 \sqrt[6]{3}}{3}$

Divide $\sqrt[6]{3}$ by $1$ .

$\sqrt[6]{3}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{3}$

Decimal Form:

$1.20093695 \dots$

Do you know how to Simplify ( cube root of 9)÷( square root of 3)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Solve for x square root of 2x+12=x-6

Solve for d A=1/2h(c+d)

Convert to Radical Form x^(4/3)

Expand log of (a*b)^2

Convert to a Decimal 57/220