Zero and Negative Exponents

Zero and Negative Exponents

Laws of Exponents

Zero Exponent

• Every time your exponent gets bigger you multiply by the base one more more time

• So every time your exponent gets smaller, you divide by the base.

• When I go from an exponent of 1 to Zero, I divide my base by itself and end up with 1 (one)

The Short Cut?!

Anything raised to the Power of Zero equals One

x⁰=1

Multiple Choice

Simplify -4x⁰

• -4

• -1

• 1

• 4

Multiple Choice

Are the following expressions equal?

 $\left(1.23491\right)^0\ =\ \left(\frac{2x}{32}\right)^0$  

• Yes 👍

• No 👎

Negative Exponents

• We already know that every time your exponent gets smaller, you divide by the base.

• So if I have an exponent smaller than zero, i.e. negative exponent, then I divide 1 by the base as many times as the exponent tells me.

•  $eg:\ 3^{-2}\ =\ 1\ \div3\div3\ =\ \frac{1}{3^2}\ or\ \frac{1}{9}$  

The Short Cut?!

Anything raised to the Power of a Negative Exponent, get the reciprocal (flip the fraction) remove the negative sign from the exponent.

Multiple Choice

Simplify: $3^{-3}$ 

•  $\frac{1}{9}$  

•  $-\frac{1}{27}$  

•  $\frac{1}{3^{-3}}$  

•  $\frac{1}{27}$  

Multiple Choice

Are the following expressions equal?

 $\left(\frac{2}{3}\right)^{-2}\ =\ \left(\frac{3}{2}\right)^2$  

• Yes 👍

• No 👎