Finite Math Examples

$\frac{2^{n + 1}}{{(2^{n})}^{n - 1}}$

Step 1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.1

Multiply the exponents in ${(2^{n})}^{n - 1}$ .

Tap for more steps...

Step 1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2^{n + 1}}{2^{n (n - 1)}}$

Step 1.1.2

Apply the distributive property.

$\frac{2^{n + 1}}{2^{n \cdot n + n \cdot - 1}}$

Step 1.1.3

Multiply $n$ by $n$ .

$\frac{2^{n + 1}}{2^{n^{2} + n \cdot - 1}}$

Step 1.1.4

Move $- 1$ to the left of $n$ .

$\frac{2^{n + 1}}{2^{n^{2} - 1 \cdot n}}$

Step 1.1.5

Rewrite $- 1 n$ as $- n$ .

$\frac{2^{n + 1}}{2^{n^{2} - n}}$

Step 1.2

Cancel the common factor of $2^{n + 1}$ and $2^{n^{2} - n}$ .

Tap for more steps...

Step 1.2.1

Factor $2^{n^{2} - n}$ out of $2^{n + 1}$ .

$\frac{2^{n^{2} - n} \cdot 2^{n + 1 - (n^{2} - n)}}{2^{n^{2} - n}}$

Step 1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.2.1

Multiply by $1$ .

$\frac{2^{n^{2} - n} \cdot 2^{n + 1 - (n^{2} - n)}}{2^{n^{2} - n} \cdot 1}$

Step 1.2.2.2

Cancel the common factor.

$\frac{2^{n^{2} - n} \cdot 2^{n + 1 - (n^{2} - n)}}{2^{n^{2} - n} \cdot 1}$

Step 1.2.2.3

Rewrite the expression.

$\frac{2^{n + 1 - (n^{2} - n)}}{1}$

Step 1.2.2.4

Divide $2^{n + 1 - (n^{2} - n)}$ by $1$ .

$2^{n + 1 - (n^{2} - n)}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$2^{n + 1 - n^{2} - - n}$

Step 2.2

Multiply $- - n$ .

Tap for more steps...

Step 2.2.1

Multiply $- 1$ by $- 1$ .

$2^{n + 1 - n^{2} + 1 n}$

Step 2.2.2

Multiply $n$ by $1$ .

$2^{n + 1 - n^{2} + n}$

Step 3

Add $n$ and $n$ .

$2^{2 n + 1 - n^{2}}$