Exponent Rules Review

When we add or subtract monomials, we...

• add the exponents

• multiply the exponents

• DO NOT CHANGE THE EXPONENTS. Add or subtract the coefficients of like terms only.

• subtract the exponents

Identify the rule:

 $a^m\cdot a^n=a^{m+n}$  

• product rule

• power rule

• quotient rule

• negative exponent rule

Identify the rule:

 $\left(a^m\right)^n=a^{m\cdot n}$  

• product rule

• power rule

• quotient rule

• negative exponent rule

Identify the rule:

 $\frac{a^m}{a^n}=a^{m-n}$  

• product rule

• power rule

• quotient rule

• negative exponent rule

Identify the rule:

 $a^{-m}=\frac{1}{a^m}\ \&\ a^m=\frac{1}{a^{-m}}$  

• product rule

• power rule

• quotient rule

• negative exponent rule

The zero exponent rule says that anything to the zero power is 1. 

For example,

 $x^0=1,\ or\ even\ \left(1,563x^2y^3z\right)^0=1$  .

This is because:

• Mathematicians just wanted to make my life more confusing.

• If I divide a number by itself, the answer is 1 and the quotient rule results in a 0 exponent.

• My teacher said so.

• Multiplying something by itself 0 times doesn't make any sense.

 $9x^2y-10x^2y=$  

•  $-90x^4y^2$  

•  $-x^4y^2$  

•  $-x^2y$  

• -1

 $\left(-2a^2b\right)\left(7a^3b\right)=$  

•  $5a^5b^2$  

•  $-14a^5b^2$  

•  $-\frac{14b^2}{a}$  

•  $-14a^6b$  

 $\left(x^2\right)^3=$  

•  $x^5$  

•  $x^{-1}$  

•  $x^{\frac{2}{3}}$  

•  $x^6$  

 $\frac{27x^5}{42x}=$  

•  $\frac{27x^6}{42}$  

•  $\frac{9}{14x^4}$  

•  $\frac{9x^{-4}}{14}$  

•  $\frac{9x^4}{14}$