Rules of Exponents

Rules of Exponents

​Multiplying
Dividing
Raising to Zeroth Power
Power to a Power
Negatives

Multiplying Bases

When multiplying the same base, the exponents are added.

Multiple Choice

 $x^4\ \cdot\ x^6$  

•  $x^2$  

•  $x^{10}$  

•  $x^{24}$  

Multiple Choice

$$4^2\ \cdot\ 4^4$$  

• $$4^8$$  

• $$4^2$$  

• $$4^6$$  

Multiple Choice

$$y^2\ \cdot\ y^4\ \cdot\ y^6$$  

• $$y^{12}$$  

• $$y^{10}$$  

• $$y^{48}$$  

Dividing Bases

When dividing the same bases, exponents are subtracted.

Multiple Choice

$$\frac{x^{10}}{x^3}$$  

• $$x^{30}$$  

• $$x^{13}$$  

• $$x^7$$  

Multiple Choice

$$\frac{3^8}{3^6}$$  

• $$3^{14}$$  

• $$3^2$$  

• $$3^{48}$$  

Multiple Choice

 $\frac{x^5\cdot y^9}{x^5\cdot y^4}$  

•  $y^5$  

•  $x\cdot y^5$  

•  $x^{10}.\ y^{13}$  

Power of Power

When raising a power to a power, exponents are multiplied.

Multiple Choice

$$\left(x^2\right)^4$$  

• $$x^8$$  

• $$x^6$$  

• $$x^2$$  

Multiple Choice

$$\left(x^2\cdot y^5\right)^3$$  

• $$x^5\cdot y^8$$  

• $$x^1\cdot y^2$$  

• $$x^6\cdot y^{15}$$  

Multiple Choice

$$\left[\left(4^2\right)^3\right]^5$$  

• $$4^{30}$$  

• $$x^{10}$$  

• $$x^{11}$$  

Negative Exponents

It is rude to leave an exponent negative.  To make an exponent positive, flip it to the other side of the fraction bar. 

Multiple Choice

 $\frac{1}{x^{-4}}$  

•  $x^3$  

•  $x^4$  

•  $x^{-4}$  

Multiple Choice

$$x^{-6}$$  

• $$\frac{1}{x^6}$$  

• $$\frac{x}{x^6}$$  

• $$x^5$$  

Multiple Choice

$$\frac{x^7\cdot y^{-4}\cdot z^{-2}}{x^4}$$  

• $$\frac{x^{11}}{y^{4\ \cdot\ }z^2}$$  

• $$\frac{x^4}{y^4\cdot z^2}$$  

• $$\frac{x^3}{y^4.\ z^2}$$  

Zero Exponents

Anything to the zeroth power is 1.  

Why are zero exponents equal to 1?

Look at the chart to see why this works.

Multiple Choice

 $16^0$  

• 16
  

•  $\frac{1}{16}$  

• 1

Multiple Choice

$$\left(2^4\right)^0$$  

• 1

• 2

• $$\frac{1}{2}$$  

Multiple Choice

$$\left(m^4\cdot n^5\cdot x^{-9}\right)^0$$  

• $$\frac{1}{x^9}$$  

• 1

• $$m\cdot n\cdot x$$