Basic Math Examples

$\frac{{(7^{n})}^{- 1} \cdot {(14^{n})}^{6}}{{(128 \cdot 7^{4})}^{n}}$

Step 1

Move ${(7^{n})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(14^{n})}^{6}}{{(128 \cdot 7^{4})}^{n} \cdot 7^{n}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite.

$\frac{{(14^{n})}^{6}}{{(128 \cdot 7^{4})}^{n} {(7^{n})}^{1}}$

Step 2.2

Rewrite ${(128 \cdot 7^{4})}^{n} \cdot 7^{n}$ as ${(128 \cdot 7^{4} \cdot 7)}^{n}$ .

$\frac{{(14^{n})}^{6}}{{(128 \cdot 7^{4} \cdot 7)}^{n}}$

Step 3

Multiply the exponents in ${(14^{n})}^{6}$ .

Tap for more steps...

Step 3.1

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

$\frac{14^{n \cdot 6}}{{(128 \cdot 7^{4} \cdot 7)}^{n}}$

Step 3.2

Move $6$ to the left of $n$ .

$\frac{14^{6 n}}{{(128 \cdot 7^{4} \cdot 7)}^{n}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $7^{4}$ by $7$ by adding the exponents.

Tap for more steps...

Step 4.1.1

Move $7$ .

$\frac{14^{6 n}}{{(128 \cdot (7 \cdot 7^{4}))}^{n}}$

Step 4.1.2

Multiply $7$ by $7^{4}$ .

Tap for more steps...

Step 4.1.2.1

Raise $7$ to the power of $1$ .

$\frac{14^{6 n}}{{(128 \cdot (7^{1} \cdot 7^{4}))}^{n}}$

Step 4.1.2.2

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

$\frac{14^{6 n}}{{(128 \cdot 7^{1 + 4})}^{n}}$

Step 4.1.3

Add $1$ and $4$ .

$\frac{14^{6 n}}{{(128 \cdot 7^{5})}^{n}}$

Step 4.2

Raise $7$ to the power of $5$ .

$\frac{14^{6 n}}{{(128 \cdot 16807)}^{n}}$

Step 4.3

Multiply $128$ by $16807$ .

$\frac{14^{6 n}}{2151296^{n}}$