Simplify 24/((2 square root of x)^3)

$\frac{24}{{(2 \sqrt{x})}^{3}}$

Simplify the denominator.

Apply the product rule to $2 \sqrt{x}$ .

$\frac{24}{2^{3} {\sqrt{x}}^{3}}$

Raise $2$ to the power of $3$ .

$\frac{24}{8 {\sqrt{x}}^{3}}$

Rewrite ${\sqrt{x}}^{3}$ as ${(x^{3})}^{\frac{1}{2}}$ .

$\frac{24}{8 \sqrt{x^{3}}}$

Factor out $x^{2}$ .

$\frac{24}{8 \sqrt{x^{2} x}}$

Pull terms out from under the radical.

$\frac{24}{8 x \sqrt{x}}$

Cancel the common factor of $24$ and $8$ .

Factor $8$ out of $24$ .

$\frac{8 \cdot 3}{8 x \sqrt{x}}$

Cancel the common factors.

Factor $8$ out of $8 x \sqrt{x}$ .

$\frac{8 \cdot 3}{8 (x \sqrt{x})}$

Cancel the common factor.

$\frac{8 \cdot 3}{8 (x \sqrt{x})}$

Rewrite the expression.

$\frac{3}{x \sqrt{x}}$

Multiply $\frac{3}{x \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{3}{x \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Combine and simplify the denominator.

Multiply $\frac{3}{x \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{3 \sqrt{x}}{x \sqrt{x} \sqrt{x}}$

Move $\sqrt{x}$ .

$\frac{3 \sqrt{x}}{x (\sqrt{x} \sqrt{x})}$

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

$\frac{3 \sqrt{x}}{x ({\sqrt{x}}^{1} \sqrt{x})}$

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

$\frac{3 \sqrt{x}}{x ({\sqrt{x}}^{1} {\sqrt{x}}^{1})}$

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

$\frac{3 \sqrt{x}}{x {\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 \sqrt{x}}{x {\sqrt{x}}^{2}}$

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

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

$\frac{3 \sqrt{x}}{x {(x^{\frac{1}{2}})}^{2}}$

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

$\frac{3 \sqrt{x}}{x \cdot x^{\frac{1}{2} \cdot 2}}$

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

$\frac{3 \sqrt{x}}{x \cdot x^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \sqrt{x}}{x \cdot x^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{3 \sqrt{x}}{x \cdot x^{1}}$

Simplify.

$\frac{3 \sqrt{x}}{x \cdot x}$

Multiply $x$ by $x$ .

$\frac{3 \sqrt{x}}{x^{2}}$

Simplify 24/((2 square root of x)^3)

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