Simplify the Radical Expression (12x^(7/2))/(3x^2)

$\frac{12 x^{\frac{7}{2}}}{3 x^{2}}$

Step 1

Move $x^{2}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{12 x^{\frac{7}{2}} x^{- 2}}{3}$

Step 2

Multiply $x^{\frac{7}{2}}$ by $x^{- 2}$ by adding the exponents.

Move $x^{- 2}$ .

$\frac{12 (x^{- 2} x^{\frac{7}{2}})}{3}$

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

$\frac{12 x^{- 2 + \frac{7}{2}}}{3}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12 x^{- 2 \cdot \frac{2}{2} + \frac{7}{2}}}{3}$

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

$\frac{12 x^{\frac{- 2 \cdot 2}{2} + \frac{7}{2}}}{3}$

Combine the numerators over the common denominator.

$\frac{12 x^{\frac{- 2 \cdot 2 + 7}{2}}}{3}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$\frac{12 x^{\frac{- 4 + 7}{2}}}{3}$

Add $- 4$ and $7$ .

$\frac{12 x^{\frac{3}{2}}}{3}$

Step 3

Factor $3$ out of $12 x^{\frac{3}{2}}$ .

$\frac{3 (4 x^{\frac{3}{2}})}{3}$

Step 4

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (4 x^{\frac{3}{2}})}{3 (1)}$

Cancel the common factor.

$\frac{3 (4 x^{\frac{3}{2}})}{3 \cdot 1}$

Rewrite the expression.

$\frac{4 x^{\frac{3}{2}}}{1}$

Divide $4 x^{\frac{3}{2}}$ by $1$ .

$4 x^{\frac{3}{2}}$