Rules of Exponents

Rules of Exponents

What do you remember?

Multiple Select

According to the exponent rules, when we raise a Power to a Power(Power Rule) we ______ the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Select

According to the product rule, when we multiply the number with exponents with the same base we _______ the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Select

The quotient law states: Keep the base the same and _________ the exponents.

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Anything raised to a power of zero is always:

• 0

• itself

• 1

• negative

Multiple Choice

Negative Exponent Law states: you must change the exponent to a positive by doing what?

• just change it to positive

• move it to the opposite side of fraction bar

Poll

How do we feel about Laws of Exponents Rules?

Multiple Choice

Simplify the expression.

 $x^4\left(x^{12}\right)$  

•  $x^3$  

•  $x^{48}$  

•  $x^{16}$  

•  $x^8$  

Multiple Choice

 Simplify 

 $\left(-4r^5\right)\left(2r^8\right)$  

•  $-2r^{13}$  

•  $-8r^{40}$  

•  $-2r^{40}$  

•  $-8r^{13}$  

Multiple Choice

Simplify: 

 $\frac{k^4}{k^3}$  

•  $k$  

•  $k^7$  

•  $k^{12}$  

•  $\frac{1}{k}$  

Multiple Choice

Simplify:

 $\frac{10h^9}{5h^7}$  

•  $\frac{2}{h^2}$  

•  $15h^{16}$  

•  $2h^2$  

•  $\frac{1}{2h^2}$  

Multiple Choice

Simplify:

 $\frac{4x^{12}y^3z^6}{2x^4y^3z}$  

•  $2x^8z^5$  

•  $\frac{2y^6}{x^3z^5}$  

•  $2x^3y^6z^5$  

•  $\frac{z^5}{2x^8}$  

Multiple Choice

Simplify:

 $\left(x^3\right)^8$  

•  $x^{11}$  

•  $x^{\frac{8}{3}}$  

•  $x^{24}$  

•  $x^5$  

Multiple Choice

Simplify:

 $\left(3xy^3\right)^2$  

•  $3x^2y^5$  

•  $9x^2y^6$  

•  $6x^2y^6$  

•  $-9x^2y^5$  

Multiple Choice

Simplify:

 $\left(2x^4y^{-3}\right)\left(-5x^{-2}y^{-1}\right)$  

•  $-\frac{10x^2}{y^4}$  

•  $-\frac{10y^4}{x^8}$  

•  $\frac{2x^2}{5y^4}$  

•  $\frac{x^2}{10y^4}$  

Multiple Choice

Simplify:

 $\left(2x^{-2}y^4\right)^3$  

•  $\frac{y^{12}}{8x^6}$  

•  $8x^6y^{12}$  

•  $\frac{8y^{12}}{x^6}$  

•  $\frac{6y^7}{x^5}$  

Multiple Choice

Simplify:

 $\frac{6x^{-2}y^3}{2x^5y^{-1}}$  

•  $\frac{3y^4}{x^7}$  

•  $\frac{4y^4}{x^7}$  

•  $8x^7y^4$  

•  $\frac{4y^4}{x^7}$  

Rational Exponents

Can you convert?

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

• 4^4/3
• 4^3/4
• 2^4/3
• 2^3/4

Multiple Choice

Simplify . Your answer should contain only positive exponents.$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$  

•  $x^{\frac{4}{3}}y^{\frac{5}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{1}{2}}$  

•  $x^{\frac{1}{3}}y^{\frac{3}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{4}{3}}$  

Multiple Choice

Simplify . Your answer should contain only positive exponents.  $\left(x^{\frac{5}{3}}y^{-2}\right)^0$  

•  $1$  

•  $\frac{x^{\frac{5}{3}}}{y^2}$  

•  $x^{\frac{5}{3}}y^2$  

•  $\frac{y^2}{x^{\frac{5}{3}}}$  

Poll

How do feel about exponents?