Calculus Examples

$\frac{\frac{1}{2} \cdot {(2 x + 5)}^{- \frac{3}{2}}}{\frac{3}{2}}$

Step 1

Move ${(2 x + 5)}^{- \frac{3}{2}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{2}}{\frac{3}{2} {(2 x + 5)}^{\frac{3}{2}}}$

Step 2

Combine $\frac{3}{2}$ and ${(2 x + 5)}^{\frac{3}{2}}$ .

$\frac{\frac{1}{2}}{\frac{3 {(2 x + 5)}^{\frac{3}{2}}}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{2}{3 {(2 x + 5)}^{\frac{3}{2}}}$

Step 4

Combine.

$\frac{1 \cdot 2}{2 (3 {(2 x + 5)}^{\frac{3}{2}})}$

Step 5

Cancel the common factor.

$\frac{1 \cdot 2}{2 (3 {(2 x + 5)}^{\frac{3}{2}})}$

Step 6

Rewrite the expression.

$\frac{1}{3 {(2 x + 5)}^{\frac{3}{2}}}$