Finite Math Examples

${(\frac{1}{6})}^{2} \cdot {(\frac{5}{6})}^{5}$

Step 1

Combine fractions.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{1}{6}$ .

$\frac{1^{2}}{6^{2}} \cdot {(\frac{5}{6})}^{5}$

Step 1.2

Simplify the expression.

Tap for more steps...

Step 1.2.1

One to any power is one.

$\frac{1}{6^{2}} \cdot {(\frac{5}{6})}^{5}$

Step 1.2.2

Raise $6$ to the power of $2$ .

$\frac{1}{36} \cdot {(\frac{5}{6})}^{5}$

Step 1.2.3

Apply the product rule to $\frac{5}{6}$ .

$\frac{1}{36} \cdot \frac{5^{5}}{6^{5}}$

$\frac{1}{36} \cdot \frac{5^{5}}{6^{5}}$

Step 1.3

Combine.

$\frac{1 \cdot 5^{5}}{36 \cdot 6^{5}}$

Step 1.4

Multiply $5^{5}$ by $1$ .

$\frac{5^{5}}{36 \cdot 6^{5}}$

$\frac{5^{5}}{36 \cdot 6^{5}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{5^{5}}{6^{2} \cdot 6^{5}}$

Step 2.2

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

$\frac{5^{5}}{6^{2 + 5}}$

Step 2.3

Add $2$ and $5$ .

$\frac{5^{5}}{6^{7}}$

$\frac{5^{5}}{6^{7}}$

Step 3

Evaluate the exponents.

Tap for more steps...

Step 3.1

Raise $5$ to the power of $5$ .

$\frac{3125}{6^{7}}$

Step 3.2

Raise $6$ to the power of $7$ .

$\frac{3125}{279936}$

$\frac{3125}{279936}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3125}{279936}$

Decimal Form:

$0.01116326 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$