# How do you simplify 15^12-15^11?

May 7, 2016

${15}^{12} - {15}^{11} = 14 \cdot {15}^{11}$
or $1.2109658 \setminus \times {10}^{14}$ if you evaluate that number on a calculator/computer.

#### Explanation:

Exponential's are repeated multiplications of one number as in
${2}^{4} = 2 \cdot 2 \cdot 2 \cdot 2 = 16$ ,
because of this it's simple to break ${15}^{12}$ into ${15}^{11} \cdot 15$.
We replace the ${15}^{12}$ with this term producing,
${15}^{12} - {15}^{11} = 15 \cdot {15}^{11} - {15}^{11}$ .
Since there is a ${15}^{11}$ in both terms we can collect like terms to get
$= {15}^{11} \left(15 - 1\right)$ .
Finishing it off we have
$= 14 \cdot {15}^{11}$
or $1.2109658 \setminus \times {10}^{14}$ if you evaluate that number on a calculator/computer.