Pre-Algebra Examples

${(2 x^{5})}^{4} \div {(8 x^{2})}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{{(2 x^{5})}^{4}}{{(8 x^{2})}^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 x^{5}$ .

$\frac{2^{4} {(x^{5})}^{4}}{{(8 x^{2})}^{2}}$

Step 2.2

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

$\frac{16 {(x^{5})}^{4}}{{(8 x^{2})}^{2}}$

Step 2.3

Multiply the exponents in ${(x^{5})}^{4}$ .

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Step 2.3.1

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

$\frac{16 x^{5 \cdot 4}}{{(8 x^{2})}^{2}}$

Step 2.3.2

Multiply $5$ by $4$ .

$\frac{16 x^{20}}{{(8 x^{2})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $8 x^{2}$ .

$\frac{16 x^{20}}{8^{2} {(x^{2})}^{2}}$

Step 3.2

Raise $8$ to the power of $2$ .

$\frac{16 x^{20}}{64 {(x^{2})}^{2}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{16 x^{20}}{64 x^{2 \cdot 2}}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{16 x^{20}}{64 x^{4}}$

Step 4

Cancel the common factor of $16$ and $64$ .

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Step 4.1

Factor $16$ out of $16 x^{20}$ .

$\frac{16 (x^{20})}{64 x^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $16$ out of $64 x^{4}$ .

$\frac{16 (x^{20})}{16 (4 x^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{16 x^{20}}{16 (4 x^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{20}}{4 x^{4}}$

Step 5

Cancel the common factor of $x^{20}$ and $x^{4}$ .

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Step 5.1

Factor $x^{4}$ out of $x^{20}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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