Precalculus Examples

${(\frac{7 x^{7}}{4 x^{2}})}^{2}$

Step 1

Cancel the common factor of $x^{7}$ and $x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $7 x^{7}$ .

${(\frac{x^{2} (7 x^{5})}{4 x^{2}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x^{2}$ out of $4 x^{2}$ .

${(\frac{x^{2} (7 x^{5})}{x^{2} \cdot 4})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{x^{2} (7 x^{5})}{x^{2} \cdot 4})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{7 x^{5}}{4})}^{2}$

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 $\frac{7 x^{5}}{4}$ .

$\frac{{(7 x^{5})}^{2}}{4^{2}}$

Step 2.2

Apply the product rule to $7 x^{5}$ .

$\frac{7^{2} {(x^{5})}^{2}}{4^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $7$ to the power of $2$ .

$\frac{49 {(x^{5})}^{2}}{4^{2}}$

Step 3.2

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 3.2.1

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

$\frac{49 x^{5 \cdot 2}}{4^{2}}$

Step 3.2.2

Multiply $5$ by $2$ .

$\frac{49 x^{10}}{4^{2}}$

Step 4

Raise $4$ to the power of $2$ .

$\frac{49 x^{10}}{16}$