Exponent Rules Application

Exponent Rules

applying the exponent rules

The Product Rule adds the exponents of the SAME base

Multiple Choice

Simplify  $h^2h^6$  .
(Make sure to write the correct answer on your notes as well!)

•  $h^8$  

•  $h^{12}$  

Multiple Choice

Select the simplified expression

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

•  $-14a^6b$  

•  $-14a^6b^2$  

•  $-14a^5b^2$  

•  $-14a^5b^{ }$  

The Quotient Rule subtracts the exponents of the SAME base. Simplify any coefficients

Multiple Choice

What will be the exponent on the simplified equation for #1?

• 4

• 5

• -4

• -5

• 6

#1

Don't forget to simplify the coefficients!

 $\frac{27x^5}{42x}\ \ \ \ \ \rightarrow\ \ \ \frac{9x^4}{14}$  

Multiple Choice

#2

 $\frac{xy^2}{y^4}$  

•  $\frac{x}{y^2}$  

•  $xy^6$  

•  $\frac{x}{y^6}$  

•  $xy^2$  

The Power Rule distributes the exponent to anything inside a parenthesis.

Remember that distribute is a special way of MULTIPLYING.

Listen to the audio to hear me walk you through problem 2: $\left(\frac{2x^3}{4x^5}\right)^2$  

•  $\frac{\left(2x^3\right)^2}{\left(4x^5\right)^2}$  
  

•  $\frac{\left(2\right)^2\left(x^3\right)^2}{\left(4\right)^2\left(x^5\right)^2}$  

•  $\frac{4\cdot x^{3\cdot2}}{16\cdot x^{5\cdot2}}$  

•  $\frac{4x^6}{16x^{10}}$  

•  $\frac{1}{4x^4}\ OR\ \frac{1}{4}x^{-4}$  

Multiple Choice

Simplify #1

 $\left(-2x^3\right)^4$  

•  $16x^{12}$  

•  $-16x^{12}$  

•  $8x^{12}$  

•  $-8x^7$  

•  $16x^7$  

The Negative exponent rule creates reciprocals. This only applies to items with negative exponents.

Multiple Choice

Problem 1:  $-5x^{-2}$  

•  $\frac{1}{25x^2}$  

•  $\frac{-5}{x^2}$  

•  $\frac{25}{x^2}$  

Did you get it wrong?

Listen to this explanation

Multiple Choice

Simplify #2. 

 $\frac{3y^2}{2x^{-2}}$  

HINT: think about where the negative exponent is.

•  $\frac{3x^2y^2}{-2}$  

•  $\frac{y^2}{6x^2}$  

•  $\frac{3x^2y^2}{2}$  

•  $x^2y^2$  

The zero exponent rule states that anything taken to the 0 power is equivalent to 1.

This is derived from the quotient rule!