Simplify (64x^(9/4))/(4x^2)

$\frac{64 x^{\frac{9}{4}}}{4 x^{2}}$

Step 1

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

$\frac{64 x^{\frac{9}{4}} x^{- 2}}{4}$

Step 2

Multiply $x^{\frac{9}{4}}$ by $x^{- 2}$ by adding the exponents.

Move $x^{- 2}$ .

$\frac{64 (x^{- 2} x^{\frac{9}{4}})}{4}$

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

$\frac{64 x^{- 2 + \frac{9}{4}}}{4}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{64 x^{- 2 \cdot \frac{4}{4} + \frac{9}{4}}}{4}$

Combine $- 2$ and $\frac{4}{4}$ .

$\frac{64 x^{\frac{- 2 \cdot 4}{4} + \frac{9}{4}}}{4}$

Combine the numerators over the common denominator.

$\frac{64 x^{\frac{- 2 \cdot 4 + 9}{4}}}{4}$

Simplify the numerator.

Multiply $- 2$ by $4$ .

$\frac{64 x^{\frac{- 8 + 9}{4}}}{4}$

Add $- 8$ and $9$ .

$\frac{64 x^{\frac{1}{4}}}{4}$

Step 3

Factor $4$ out of $64 x^{\frac{1}{4}}$ .

$\frac{4 (16 x^{\frac{1}{4}})}{4}$

Step 4

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (16 x^{\frac{1}{4}})}{4 (1)}$

Cancel the common factor.

$\frac{4 (16 x^{\frac{1}{4}})}{4 \cdot 1}$

Rewrite the expression.

$\frac{16 x^{\frac{1}{4}}}{1}$

Divide $16 x^{\frac{1}{4}}$ by $1$ .

$16 x^{\frac{1}{4}}$