Basic Math Examples

$(y^{\frac{5}{7}}) (y^{\frac{1}{3}})$

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

Step 4.2

Multiply $7$ by $3$ .

$y^{\frac{5 \cdot 3}{21} + \frac{1}{3} \cdot \frac{7}{7}}$

Step 4.3

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

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

Step 4.4

Multiply $3$ by $7$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$y^{\frac{15 + 7}{21}}$

Step 6.2

Add $15$ and $7$ .

$y^{\frac{22}{21}}$