Negative and Zero Exponents

Zero Exponents, Negative Exponents, and Product Rule

Zero Exponent Rule

• Anything raised to the power zero is 1

• a⁰=1

Multiple Choice

$$\left(2x\right)^0$$  

• 0

• 1

• 2x

• 2

Multiple Choice

$$\left(x^2y^3\right)^0$$  

• 0

• 1

• $$x^2y^3$$  

Multiple Choice

$$\left(\frac{\left(x^3y^5\right)\left(xy\right)^2}{x^2y^6}\right)^0$$  

• 0

• 1

Negative Exponents

• Turn into a fraction (if its not already)

• Bring the power with the negative exponent to the opposite side of the fraction (top or bottom)

• Change the exponent to positive

•  $a^{-m}=\frac{1}{a^m}$  

Multiple Choice

$$x^{-2}$$  

• $$x^2$$  

• $$\frac{1}{x^2}$$  

• $$\frac{1}{x^{-2}}$$  

Multiple Choice

$$x^3y^{-4}$$  

• $$\frac{x^3}{y^4}$$  

• $$\frac{x^3}{y^{-4}}$$  

• $$\frac{1}{x^3y^4}$$  

Multiple Choice

$$\frac{c^{-3}}{d^{-2}}$$  

• $$\frac{d^2}{c^3}$$  

• $$\frac{1}{c^3d^2}$$  

• $$c^3d^2$$  

Product Rule

• add the exponents for the bases that are the same

•  $a^m\cdot a^n=a^{m+n}$  

Multiple Choice

$$x^4\cdot x^3$$  

• $$x^7$$  

• $$x^{12}$$  

Multiple Choice

$$\left(x^2y^3\right)\left(x^4y^3\right)$$  

• $$x^6y^6$$  

• $$x^8y^9$$