Pre-Algebra Examples

$x^{\frac{1}{7}} \cdot x^{\frac{5}{3}}$

Step 1

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

$x^{\frac{1}{7} + \frac{5}{3}}$

Step 2

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{\frac{1}{7} \cdot \frac{3}{3} + \frac{5}{3}}$

Step 3

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x^{\frac{1}{7} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{7}{7}}$

Step 4

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{7}$ by $\frac{3}{3}$ .

$x^{\frac{3}{7 \cdot 3} + \frac{5}{3} \cdot \frac{7}{7}}$

Step 4.2

Multiply $7$ by $3$ .

$x^{\frac{3}{21} + \frac{5}{3} \cdot \frac{7}{7}}$

Step 4.3

Multiply $\frac{5}{3}$ by $\frac{7}{7}$ .

$x^{\frac{3}{21} + \frac{5 \cdot 7}{3 \cdot 7}}$

Step 4.4

Multiply $3$ by $7$ .

$x^{\frac{3}{21} + \frac{5 \cdot 7}{21}}$

Step 5

Combine the numerators over the common denominator.

$x^{\frac{3 + 5 \cdot 7}{21}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $7$ .

$x^{\frac{3 + 35}{21}}$

Step 6.2

Add $3$ and $35$ .

$x^{\frac{38}{21}}$