Multiplication Property of Exponents

Multiple Choice

Which expression below is equivalent to $$\frac{x^6}{x^3}$$ ?

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

• $$\left(x\cdot x\right)\left(x\cdot x\right)\left(x\cdot x\right)$$

• $$\frac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}$$

• $$x^{\left(\frac{6}{3}\right)}$$

Rules of Exponents Review

Multiplication Property of Exponents: 

when multiplying same bases raised to different exponents, we

ADD the exponents.

Multiplication Property of Exponents: 

Math Response

So, if $$x^4\cdot x^2=\left(x\cdot x\cdot x\cdot x\right)\cdot\left(x\cdot x\right)$$ , then $$x^4\cdot x^2=$$

Type answer here

Correct Answer: x^6

Deg^°

Rad

Multiple Choice

Evaluate: $$a^5\cdot a^7=$$

• $$a^{35}$$

• $$a^{12}$$

• $$a^2$$

• $$\frac{1}{a^2}$$

Multiple Choice

Evaluate: $$2^3\cdot2^5$$

• $$2^8=256$$

• $$2^{15}=32,768$$

• $$4^8=65,\ 536$$

• $$4^{15}\sim1.1\ billion$$

Division Property of Exponents: 

​When dividing same bases raised to different exponents, we

SUBTRACT the exponents.

Division Property of Exponents: 

Math Response

Simplify: $$\frac{8x^{12}}{4x^6}$$

Type answer here

Correct Answer: 2x^6

Deg^°

Rad

Multiple Choice

Simplify: $$\frac{2^8}{2^4}$$

• $$1$$

• $$4$$

• $$16$$

• $$\frac{1}{2}$$

Power Property of Exponents: 

when a base raised to one power is raised to another power, we MULTIPLY the exponents

Power Property of Exponents: 

Multiple Choice

Evaluate: $$\left(x^3\right)^5$$

• $$x^8$$

• $$x^{15}$$

• $$x^{125}$$

• $$5x^3$$

Multiple Select

Which of the following expressions are equivalent to $$4^5$$ ?

• $$2^{10}$$

• $$1024$$

• $$20$$

• $$2^{20}$$

Zero Exponent Property: 

What is the value when we raise something to the power of 0?

Multiple Choice

So, since $$\frac{x^5}{x^5}$$ simplifies BOTH to $$x^0$$ AND also to $$1$$ , we can safely conclude that $$x^0$$ = ?

• 1

• 0

• $$\frac{1}{x}$$

Zero Exponent Property: 

Negative Exponent Property: 

What does it mean when we raise something to a negative exponent?

Multiple Choice

So, since $$\frac{x^2}{x^5}$$ simplifies BOTH to $$x^{-3}$$ AND also to $$\frac{1}{x^3}$$ , we can safely conclude that $$x^{-3}$$ = ?

• -3x

• $$\frac{-3}{x}$$

• $$\frac{1}{x^3}$$

Negative Exponent Property: 

In summary, a base raised to a negative exponent means that there are that many factors of the base in the denominator.

Additionally,

So, essentially, a negative exponent implies a reciprocal.

Multiple Choice

Which of the expressions below is equivalent to $$x^{-8}$$ ?

• $$-8x$$

• $$\frac{-8}{x}$$

• $$-x^8$$

• $$\frac{1}{x^8}$$

Multiple Choice

Evaluate: $$6^{-2}$$

• -12

• -36

• $$\frac{1}{36}$$

Multiple Choice

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

• $$\frac{1}{32}$$

• $$-\frac{1}{32}$$

• $$32$$

• $$-32$$

Here are two more things you CAN do with exponents:

Lastly here is the one thing CANNOT do with exponents:

Here are a few more practice questions

Math Response

$$\left(5x^4\right)\left(6x^2\right)=$$

Type answer here

Correct Answer: 30x^6

Deg^°

Rad

Multiple Choice

Simplify $$\frac{8y^9}{6y^3}=$$

• $$\frac{4}{3y^3}$$

• $$\frac{8y^3}{6}$$

• $$\frac{4y^6}{3}$$

Math Response

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

Type answer here

Correct Answer: 16x^8y^{12}

Deg^°

Rad

Multiple Choice

Simplify: $$\left(\frac{ab^2}{c^3}\right)^5=$$

• $$\frac{a^5b^{10}}{c^5}$$

• $$\frac{a^5b^{10}}{c^{15}}$$

• $$\frac{ab^2}{c^3}$$

• $$\frac{5ab^2}{c^3}$$

Math Response

Simplify: $$\left(-3x^2y^{-4}\right)\left(5x^{-1}y^8\right)\left(x^0\right)=$$

Type answer here

Correct Answer: -15xy^4

Deg^°

Rad

Multiple Choice

Simplify: $$\left(10m^4n^2\right)^{-3}=$$

• $$-30m^{12}n^6$$

• $$\frac{1}{1000m^{12}n^6}$$

• $$\frac{-30m}{n}$$

• $$-1000m^{12}n^6$$

Multiple Choice

Evaluate: $$\left(x-9\right)^2=$$

• $$x^2-81$$

• $$x^2+81$$

• $$x^2-18x+81$$

• $$x^2+18x+81$$