Equivalent Equations

Algebra 1

Unit 2, Lesson 2

Applying Quotient
Laws of Exponents to Algebraic
Expressions

Volume 1, pg. 61

Benchmark & Learning Target

volume 1, pg. 61

MA.912.NSO.1.2

Generate equivalent algebraic expressions
using the properties of exponents.

​❑ I can generate equivalent algebraic expressions to find the quotient of two monomials using the properties (laws) of exponents.

2.2.2 Guided Instruction: Quotient of Powers

volume 1, pg. 62

volume 1, pg. 62

​You'll submit your answer on the next slide

Multiple Choice

Finish simplifying $$\frac{x^2}{x^5}$$

• $$x^3$$

• $$\frac{1}{x^3}$$

• $$\frac{1}{x^{-3}}$$

• $$x^{\frac{2}{5}}$$

Labelling

Label the numerator and denominator

Drag labels to their correct position on the image

Denominator

Numerator

volume 1, pg. 63

You will use the quotient of powers law in the next few questions!

​If you're not getting it, watch this video that helps break down how to divide monomials

Math Response

Use the quotient of powers law to find an equivalent expression for $$\frac{x^2}{x^5}$$

Type answer here

Correct Answer: \frac{1}{x^5}

Deg^°

Rad

Labelling

Use the property of exponents to find an equivalent expression $$\frac{x^3y^{11}z^3}{x^2y^2}$$ . Drag the exponents to their correct spot.

Drag labels to their correct position on the image

1

3

13

9

5

What happened to z?

Note that the power of z did not change. This is because it did not have a "like term" in the denominator. If there is only one variable, then it and its exponent stay the same.

volume 1, pg. 63

​You will type in your answer on the next slide, so be ready!

Math Response

Determine an equivalent expression to $$\frac{12x^3y^1}{6x^1y^3}$$

Type answer here

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

Deg^°

Rad

Multiple Choice

Write an expression equivalent to $$\frac{12s^5t^9}{20t^3}$$

• $$\frac{3s^5t^6}{5}$$

• $$\frac{3t^6}{5}$$

• $$\frac{3s^5t^3}{5}$$

• $$\frac{s^5t^6}{8}$$

Multiple Choice

Now that we have found the equivalent expression $$\frac{3s^5t^6}{5}$$ , is there a domain restriction?

• Yes

• No

Multiple Choice

Write an expression which is equivalent to $$\frac{21a^8b^3c^{15}}{7a^3b^{12}c^2}$$

• $$3a^5c^{13}b^9$$

• $$\frac{3a^5c^{13}}{b^9}$$

• $$\frac{14a^5c^{13}}{b^9}$$

• $$14a^5b^4c^{13}$$

Multiple Choice

Now that we have found the equivalent expression, $$\frac{3a^5c^{13}}{b^9}$$ , is there a domain restriction?

• No

• Yes, $$b\ne0$$

• Yes, $$b\ne9$$

Multiple Choice

Write an expression equivalent to $$\frac{3nm^4}{6n^2m^7}$$

• $$2nm^3$$

• $$\frac{1}{2n^2m^3}$$

• $$\frac{1}{2nm^3}$$

• $$\frac{2}{n^2m^3}$$

Multiple Choice

Now that we have the equivalent expression, $$\frac{1}{2nm^3}$$ , is there a domain restriction?

• Yes

• No

Multiple Select

Select all that would be domain restrictions for $$\frac{1}{2nm^3}$$

• $$n\ne0$$

• $$m\ne0$$

• $$n\ne-2$$

• $$m\ne2$$

2.2.4 Guided Instruction: Power of a Quotient

volume 1, pg. 65

1.

Three students generated equivalent expressions using exponent laws.

a.

Finish Amir’s work using a similar strategy to the one used by Luis and
Maya.

Multiple Choice

Finish Amir's work to simplify $$\left(\frac{7c}{r}\right)^3$$

• $$\frac{21c^3}{r^3}$$

• $$\frac{7c}{r}$$

• $$\frac{343c^3}{r^3}$$

• $$\frac{7c^3}{r^3}$$

Multiple Select

Select which expression(s) would have domain restrictions

• $$\left(\frac{3}{11}\right)^5=\frac{3^5}{11^5}$$

• $$\left(\frac{x}{6y}\right)^2=\frac{x^2}{36y^2}$$

• $$\left(\frac{7c}{r}\right)^3=\frac{343c^3}{r^3}$$

Match

Match each expression to an equivalent expression

• $$\frac{a^2b^3}{-4b^3}$$

• $$\left(\frac{8ay}{3bp}\right)^3$$

• $$\frac{-18a^{12}by^4}{9a^9y^4}$$

• $$\frac{20a^5}{11b^3p^6}$$

• $$\frac{1}{a^5b^4}$$

• $$\frac{a^2}{-4}$$

• $$\frac{612a^3y^3}{27b^3p^3}$$

• $$-2a^3b$$

• $$\frac{100a^6p^7y}{55ab^3p^{13}y}$$

• $$\frac{a^{20}b^7p^0}{a^{25}b^{11}}$$