Pre-Algebra Examples

$\frac{40 x^{\frac{1}{5}}}{5 x^{\frac{1}{8}}}$

Step 1

Move $x^{\frac{1}{8}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{40 x^{\frac{1}{5}} x^{- \frac{1}{8}}}{5}$

Step 2

Multiply $x^{\frac{1}{5}}$ by $x^{- \frac{1}{8}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{1}{8}}$ .

$\frac{40 (x^{- \frac{1}{8}} x^{\frac{1}{5}})}{5}$

Step 2.2

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

$\frac{40 x^{- \frac{1}{8} + \frac{1}{5}}}{5}$

Step 2.3

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{40 x^{- \frac{1}{8} \cdot \frac{5}{5} + \frac{1}{5}}}{5}$

Step 2.4

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{40 x^{- \frac{1}{8} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{8}{8}}}{5}$

Step 2.5

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{1}{8}$ by $\frac{5}{5}$ .

$\frac{40 x^{- \frac{5}{8 \cdot 5} + \frac{1}{5} \cdot \frac{8}{8}}}{5}$

Step 2.5.2

Multiply $8$ by $5$ .

$\frac{40 x^{- \frac{5}{40} + \frac{1}{5} \cdot \frac{8}{8}}}{5}$

Step 2.5.3

Multiply $\frac{1}{5}$ by $\frac{8}{8}$ .

$\frac{40 x^{- \frac{5}{40} + \frac{8}{5 \cdot 8}}}{5}$

Step 2.5.4

Multiply $5$ by $8$ .

$\frac{40 x^{- \frac{5}{40} + \frac{8}{40}}}{5}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{40 x^{\frac{- 5 + 8}{40}}}{5}$

Step 2.7

Add $- 5$ and $8$ .

$\frac{40 x^{\frac{3}{40}}}{5}$

Step 3

Factor $5$ out of $40 x^{\frac{3}{40}}$ .

$\frac{5 (8 x^{\frac{3}{40}})}{5}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $5$ out of $5$ .

$\frac{5 (8 x^{\frac{3}{40}})}{5 (1)}$

Step 4.2

Cancel the common factor.

$\frac{5 (8 x^{\frac{3}{40}})}{5 \cdot 1}$

Step 4.3

Rewrite the expression.

$\frac{8 x^{\frac{3}{40}}}{1}$

Step 4.4

Divide $8 x^{\frac{3}{40}}$ by $1$ .

$8 x^{\frac{3}{40}}$