Properties of Exponents

Properties of Exponents

Zero and Negative Exponents

• Anything with a 0 exponent is just 1

• With a negative exponent, make it positive by moving

• Move to other side of fraction

Multiple Choice

Anything with an Exponent of Zero is just what number?

for example (-32154636xyzre)⁰ would equal what?

• 0

• 1

• 2

• 3

Multiple Choice

Simplify the expression..
 $\left(-9\right)^0$  

• -9

• 0

• 1

• 9

Multiple Choice

Simplify..

 $3^{-3}$  

•  $\frac{1}{3^3}$  

•  $\frac{1}{27}$  

•  $27$  

•  $\frac{1}{9}$  

Multiple Choice

Simplify..

 $\frac{-5^0}{2^{-2}}$  

•  $\frac{5}{2}$  

• 4

•  $\frac{1}{4}$  

Product & Quotient of Powers

• When you multiply two of the same number ADD the Exponents

• When you divide two of the same number SUBTRACT the Exponents

Multiple Choice

Simplify..

 $2^3\cdot2^4$  

• 4096

•  $2^7$  

• 128

•  $2^7$  

Multiple Choice

Simplify..

 $m^{10}\cdot m^5$  

•  $m^{15}$  

•  $m^{50}$  

Multiple Choice

Simplify...

 $3^{10}\cdot3^{-10}$  

•  $3^{20}$  

• 1

•  $3^{10}$  

Multiple Choice

Simplify...

 $\frac{5^6}{5^2}$  

•  $\frac{1}{625}$  

•  $5^4$  

• 625

Multiple Choice

Simplify...

 $\frac{2^3}{2^8}$  

•  $2^5$  

•  $\frac{1}{32}$  

Multiple Choice

Simplify...

 $\frac{x^9}{x^5}$  

•  $x^{14}$  

•  $x^4$  

•  $x^5$  

Power of a Power

Distribute the exponent outside the parentheses to every exponent inside the parentheses

Multiple Choice

Simplify...

 $\left(w^{12}\right)^5$  

•  $w^{17}$  

•  $w^{60}$  

•  $w^7$  

Multiple Choice

Simplify...

 $\left(w^{-3}\right)^2$  

•  $\frac{1}{w^6}$  

•  $w^6$  

•  $\frac{1}{w^5}$  

•  $w^5$  

Multiple Choice

Simplify...

 $\left(p^6\right)^4$  

•  $p^{24}$  

•  $p^{10}$  

•  $p^2$  

Power of a Product

Distribute the Exponent to everything inside.

Multiple Choice

Simplify...

 $\left(-5z\right)^3$  

•  $-15z^3$  

•  $-125z^3$  

•  $-5z^3$  

Multiple Choice

Simplify...

 $\left(4x\right)^{-4}$  

•  $\frac{1}{256x^4}$  

•  $256x^{-4}$  

•  $16x^{-4}$  

•  $\frac{1}{16x^4}$  

Power of a Quotient

Like power of a power, distribute the exponent to every exponent inside the parentheses.

Multiple Choice

Simplify...

 $\left(\frac{6}{n}\right)^2$  

•  $\frac{12}{n^2}$  

•  $\frac{36}{n^2}$  

Multiple Choice

Simplify...

 $\left(\frac{1}{2k^2}\right)^5$  

•  $\frac{5}{10k^7}$  

•  $\frac{1}{2^5k^2}$  

•  $\frac{1}{32k^{10}}$  

Simplifying using Properties of Exponents

Exponents change exponents, Bases change bases.

Remember,

Little Numbers to Little Numbers - Big Numbers to Big Numbers

When simplifying, it might be possible to use multiple properties.