Calculus Examples

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

Step 1

Combine $\frac{3}{2}$ and $x^{\frac{1}{2}}$ .

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

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{3 x^{\frac{1}{2}}}{2}$ .

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

Step 2.2

Apply the product rule to $3 x^{\frac{1}{2}}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{9 {(x^{\frac{1}{2}})}^{2}}{2^{2}}$

Step 3.2

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1

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

$\frac{9 x^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{9 x^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 3.2.2.2

Rewrite the expression.

$\frac{9 x^{1}}{2^{2}}$

Step 3.3

Simplify.

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

Step 4

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

$\frac{9 x}{4}$