Rules of Exponents

Rules of Exponents Lesson

Math IV

Product Rule

• Same base- ADD the exponents

Multiple Choice

 $x^5\ \cdot\ x^3$  

•  $x^{15}$  

•  $x^8$  

•  $x^{\frac{5}{3}}$  

•  $x^2$  

Quotient Rule

• Same base- SUBTRACT the exponents

Multiple Choice

 $\frac{x^9}{x^5}$  

•  $x^{14}$  

•  $x^{-4}$  

•  $x^4$  

•  $x^{\frac{9}{5}}$  

Power Rule

• Power raised to a power- MULTIPLY the exponents

Multiple Choice

 $\left(x^3\right)^4$  

•  $x^{\frac{3}{4}}$  

•  $x^{81}$  

•  $x^7$  

•  $x^{12}$  

Power of a Product Rule

• Product to a power- DISTRIBUTE to each base

• Raise the number to the exponent

• Multiply exponents

Multiple Choice

 $\left(4x^3\right)^2$  

•  $16x^6$  

•  $8x^6$  

•  $16x^5$  

•  $8x^5$  

Quotient of a Power Rule

• Distribute the exponent to the numerator and denominator

Multiple Choice

 $\left(\frac{x}{y}\right)^2$  

•  $\frac{x^2}{y}$  

•  $\frac{x^2}{y^2}$  

•  $x^2$  

•  $y^2$  

Negative Exponent Rule

• Flip and change sign to positive

• If the negative is in the numerator move it to the denominator

• If the negative is the denominator move it to the numerator

Multiple Choice

 $x^{-3}$  

•  $x^3$  

• 1

•  $\frac{1}{x^3}$  

Multiple Choice

 $\frac{1}{x^{-5}}$  

•  $\frac{1}{x^5}$  

•  $2x^5$  

• 1

•  $x^5$  

Zero Exponent Rule

• Anything to the power of zero is equal to 1

Multiple Choice

 $\left(-4x\right)^0$  

• -1

• 1

• 0

• -4

Now let's put all the rules together.

Practice Problems

Multiple Choice

 $-4^0$  

• 1

• -1

• 0

• 4

Multiple Select

 $5^{-3}$   Check all that apply.

• 125

•  $\frac{1}{5^3}$  

•  $\frac{1}{125}$  

• -15

Multiple Choice

 $4a^3\ \cdot\ 2a^4$  

•  $8a^7$  

•  $8a^{12}$  

•  $6a^7$  

•  $6a^{12}$  

Multiple Choice

 $3a^2b^{-4}$  

•  $\frac{3a^2}{b^4}$  

•  $3a^2b^4$  

•  $\frac{3b^4}{a^2}$  

Multiple Choice

 $\left(4a^3\right)^4$  

•  $16a^{12}$  

•  $16a^7$  

•  $256a^7$  

•  $256a^{12}$  

Multiple Choice

 $\frac{10z^5}{5z^2}$  

•  $5z^3$  

•  $2z^3$  

•  $5z^7$  

•  $15z^7$  

Multiple Choice

 $\left(x^5y^6\right)^2$  

•  $x^7y^8$  

•  $x^{10}y^{12}$  

•  $x^{25}y^{36}$  

•  $x^3y^4$  

Multiple Choice

 $\frac{\left(xy\right)^5}{x}$  

•  $x^4y^5$  

•  $x^5y^5$  

•  $\frac{x^5y^5}{x}$  

•  $xy^5$  

Multiple Choice

 $\frac{x^{-3}y^2}{6^{-2}}$  

•  $\frac{x^3y^2}{36}$  

•  $-\frac{36y^2}{x^{-3}}$  

•  $\frac{36y^2}{x^3}$  

Multiple Choice

 $\left(a^3\right)^{-2}$  

•  $a^{-6}$  

•  $\frac{1}{a^6}$  

•  $a^6$  

• -6

Multiple Choice

 $2^3\cdot2^5\cdot2^0$  

•  $2^8$  

• 1

•  $2^{15}$  

•  $8^8$  

Multiple Choice

 $\frac{2ab^4\cdot c}{\left(ba^{-4}\right)^2}$  

•  $2a^9b^2c$  

•  $4ab^2$  

•  $\frac{2ab^4c}{b^2a^{-8}}$  

Poll

Do you understand the rules of exponents?

• GOT IT!

• ALMOST GOT IT!

• TOTALLY LOST!