Laws of Exponents

Simplifying Expressions with Exponents

Open Ended

Any base (except 0) raised to the power of zero is what?!?

Multiple Choice

Simplify

$$\left(\frac{2^0}{3^2}\right)^{ }$$  

• $$\frac{1}{9}$$  

• 1

• 49

• $$\frac{6}{1}$$  

Multiple Choice

Simplify

$$\left(x^9\times x^{-7}\right)^0\times y^2$$  

• 1

•   $$x^{-63}y^2$$  

• $$x^2y^2$$  

• $$y^2$$  

Math Response

Simplify

$$\left(8x^{-4}y^{-3}\right)\left(-2x^5y^6\right)$$

Type answer here

Correct Answer: -16xy^3

Deg^°

Rad

Math Response

Simplify

$$\left(-3x^4y^{-3}\right)\left(-10x^{-2}y^6\right)$$

Type answer here

Correct Answer: 30x^2y^3

Deg^°

Rad

Multiple Choice

Simplify the following expression  $$\frac{-48c^2d^4}{-8cd}$$  

• $$6cd^3$$  

• $$-6cd^3$$  

• $$6c^3d^5$$  

• 1

Multiple Choice

Simplify

$$\frac{15x^{12}}{5x^7}\times\left(-3^0\right)\times x^2$$  

• $$-3x^{17}$$  

• $$-3x^5$$  

• $$3x^7$$  

• $$-1$$  

Multiple Choice

Simplify

$$\left(3xy^2\right)^2\left(x^2y\right)^4\$$  

• $$\left|x^3\right|$$  

• $$3x^{10}y^8$$  

• $$3x^4y^4$$  

• $$9x^{10}y^8$$  

Math Response

What does this expression simplify to?

$$\frac{2x^9}{2\left(x^3\right)^3}$$  

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

Simplify the expression  $$\left(\frac{3m^2n^7}{m}\right)^5$$  

Type answer here

Correct Answer:

Deg^°

Rad

Math Response

Simplify the expression  $$\left(\frac{3x^2y^7}{x}\right)^5$$  

Type answer here

Correct Answer: 243x^5y^{35}

Deg^°

Rad

Math Response

Simplify the expression.

$$\left(\frac{x}{y^2}\right)^{-2}$$  

Type answer here

Correct Answer: \frac{y^4}{x^2}

Deg^°

Rad

Multiple Select

Which of the following expressions simplify to

$$-\frac{1}{64}$$  

• $$\left(-4\right)^{-3}$$  

• $$-\left(4\right)^{-3}$$  

• $$-\frac{1}{4^3}\times-\left(4\right)^0$$  

• $$\frac{1}{\left(-4\right)^{-3}}$$  

Math Response

Simplify the following expressions. (Final answer should have positive integer exponent only.) $$\left(8x^{-4}y^3\right)\left(-2x^5y^{-6}\right)^2$$

Type answer here

Correct Answer: \frac{32x^6}{y^9}

Deg^°

Rad

Poll

How do you feel about the laws of exponents?

• Most of them confuse me still

• I just need more practice

• Only 1 or 2 laws are giving me trouble

• I fully understand the laws of exponents

Multiple Select

Which laws are still confusing if any?  SELECT ALL THAT APPLY

• Product Rule $$4^3\times4^2=4^{3+2}$$  

• Power Rule $$\left(4^2\right)^3=4^{2\times3}$$  

• Quotient Rule  $$\frac{4^5}{4^3}=4^{5-3}$$  

• Negative Rule  $$4^{-6}=\frac{1}{4^6}$$