Basic Math Examples

$\frac{{6.5}^{- \frac{1}{20}}}{{6.5}^{- \frac{3}{10}}}$

Step 1

Move ${6.5}^{- \frac{3}{10}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${6.5}^{- \frac{1}{20}} \cdot {6.5}^{\frac{3}{10}}$

Step 2

Multiply ${6.5}^{- \frac{1}{20}}$ by ${6.5}^{\frac{3}{10}}$ by adding the exponents.

Tap for more steps...

Step 2.1

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

${6.5}^{- \frac{1}{20} + \frac{3}{10}}$

Step 2.2

To write $\frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${6.5}^{- \frac{1}{20} + \frac{3}{10} \cdot \frac{2}{2}}$

Step 2.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

Multiply $\frac{3}{10}$ by $\frac{2}{2}$ .

${6.5}^{- \frac{1}{20} + \frac{3 \cdot 2}{10 \cdot 2}}$

Step 2.3.2

Multiply $10$ by $2$ .

${6.5}^{- \frac{1}{20} + \frac{3 \cdot 2}{20}}$

Step 2.4

Combine the numerators over the common denominator.

${6.5}^{\frac{- 1 + 3 \cdot 2}{20}}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $3$ by $2$ .

${6.5}^{\frac{- 1 + 6}{20}}$

Step 2.5.2

Add $- 1$ and $6$ .

${6.5}^{\frac{5}{20}}$

Step 2.6

Cancel the common factor of $5$ and $20$ .

Tap for more steps...

Step 2.6.1

Factor $5$ out of $5$ .

${6.5}^{\frac{5 (1)}{20}}$

Step 2.6.2

Cancel the common factors.

Tap for more steps...

Step 2.6.2.1

Factor $5$ out of $20$ .

${6.5}^{\frac{5 \cdot 1}{5 \cdot 4}}$

Step 2.6.2.2

Cancel the common factor.

${6.5}^{\frac{5 \cdot 1}{5 \cdot 4}}$

Step 2.6.2.3

Rewrite the expression.

${6.5}^{\frac{1}{4}}$

Step 3

Raise $6.5$ to the power of $\frac{1}{4}$ .

$1.59671843$