Calculus Examples

${(x y^{- \frac{b}{2}})}^{\frac{b}{2}}$

Step 1

Apply the product rule to $x y^{- \frac{b}{2}}$ .

$x^{\frac{b}{2}} {(y^{- \frac{b}{2}})}^{\frac{b}{2}}$

Step 2

Multiply the exponents in ${(y^{- \frac{b}{2}})}^{\frac{b}{2}}$ .

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Step 2.1

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

$x^{\frac{b}{2}} y^{- \frac{b}{2} \cdot \frac{b}{2}}$

Step 2.2

Multiply $- \frac{b}{2} \cdot \frac{b}{2}$ .

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Step 2.2.1

Multiply $\frac{b}{2}$ by $\frac{b}{2}$ .

$x^{\frac{b}{2}} y^{- \frac{b \cdot b}{2 \cdot 2}}$

Step 2.2.2

Raise $b$ to the power of $1$ .

$x^{\frac{b}{2}} y^{- \frac{b^{1} b}{2 \cdot 2}}$

Step 2.2.3

Raise $b$ to the power of $1$ .

$x^{\frac{b}{2}} y^{- \frac{b^{1} b^{1}}{2 \cdot 2}}$

Step 2.2.4

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

$x^{\frac{b}{2}} y^{- \frac{b^{1 + 1}}{2 \cdot 2}}$

Step 2.2.5

Add $1$ and $1$ .

$x^{\frac{b}{2}} y^{- \frac{b^{2}}{2 \cdot 2}}$

Step 2.2.6

Multiply $2$ by $2$ .

$x^{\frac{b}{2}} y^{- \frac{b^{2}}{4}}$