Rules of Exponents

Rules of Exponents

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Things to remember with negative exponents:

1. If an exponent is negative and it is on the numerator, then it needs to move to the denominator to make it positive.

2. If an exponent is negative and it is in the denominator, then it needs to move to the numerator to make it positive.

Remember:

Remember:

Multiple Select

When the bases are being divided, you multiply the exponents.

• TRUE

• FALSE

Fill in the Blank

When the bases are being multiplied, you ___________ the exponents.

Fill in the Blank

When you have a base raised to an exponent, and then raised to another power outside of the parentheses, you ___________ the exponents.

Open Ended

Explain in words how you would get rid of the negative exponent in the following expression:

$$3^{-2}$$  

Multiple Select

Any base raised to the power of 0 is always:

• 0

• 1

Remember:

• When bases are being multiplied, you add the exponents.

• If you have constants in the base with the variables, you multiply them.

Multiple Select

Simplify:

$$\left(5^2\right)\left(5^{-1}\right)$$  

• $$5^{-3}$$  

• $$5^1$$  

Multiple Select

Select ALL expressions that are equivalent to   $$-2^3$$  

• 8

• $$\frac{-1}{8}$$  
  

• $$\frac{-1}{2^{-3}}$$  

• $$\frac{1}{\left(-2\right)^{-3}}$$  

• $$\frac{1}{8}$$  

Multiple Choice

Simplify, remember you cannot have any negative exponents in your answer!

$$\left(2x^{-2}y^3\right)^2$$  

• $$2x^0y^5$$  

• $$\frac{2y^6}{x^4}$$  

• $$\frac{4y^6}{x^4}$$  

• $$\frac{4}{x^4y^6}$$  

Multiple Choice

$$\left(2a^2b^4c\right)\left(6a^3b^2c^5\right)$$  

Simplify:

• $$8a^5b^6c^6$$  

• $$12a^5b^6c^6$$  

• $$12a^6b^8c^5$$  

• $$8a^6b^8c^5$$  

Multiple Choice

$$\left(2x^4y^7\right)^3$$  

Simplify:

• $$6x^7y^{10}$$  

• $$8x^{12}y^{21}$$  

• $$6xy^{32}$$  

• $$8x^7y^{10}$$  

Multiple Choice

$$\frac{-12x^4y^3}{3xy^2}$$  

Simplify:

• $$-15x^5y^5$$  

• $$-4x^5y^5$$  

• $$-9x^3y$$  

• $$-4x^3y$$  

Open Ended

Samiah said that

$$\frac{3^2}{9^2}$$  simplifies to  $$\frac{1}{9}$$  .  Is she correct?  You must justify your answer!

Poll

After completing this assignment, how confident are you in using the rules of exponents to simplify expressions?

• Great, I've got this!

• I am more confident than I was yesterday.

• ok, I still need to practice

• I need to come to tutoring for help before the SBF!!