Law of Exponents: Product and Quotient Rule

Presentation

•

Mathematics

•

10th Grade

•

Hard

Joseph Anderson

FREE Resource

13 Slides • 12 Questions

LAWS OF EXPONENTS

Weekly Objective: Students will use reasoning to define the laws of exponents to simplify expressions with exponents by applying the including:

----Product Rule
----Quotient Rule
--Power Rule

with an at least 75% accuracy.

True Meaning of Exponent

Product Rule

Vocabulary Review

Base:
a number that is raised to a certain power

Exponent:
Shows how many times the number is multiplied by itself.

Coefficient:
a number that multiplied by the variable

Exponents

Let's review exponents!

Product Rule

Quotient Rule

Power Rule Investigation

Hint: Utilize expansion to help determine

Could you create a rule to simplify the expression?

Rule:

Power Rules: Investigation

Power to a Power rule

Power Rule

Multiple Choice

Simplify the following expression:

(b³)⁸

b¹¹

8b³

b²⁴

24b

Multiple Choice

Which shows the Power Rule used correctly? $\left(ab\right)^5$

$ab^5$

$a^5b^5$

$a^5b$

$a^6b^6$

Multiple Choice

$\left(x^5y^7\right)^3\ =\ x^{15}y^{21}$

True

False

Multiple Choice

Simplify the exponential expression. $\left(\left(-2\right)^5\right)^8$

$\left(-2\right)^{40}$

$\left(-2\right)^{13}$

$\left(-2\right)^3$

$\left(-2\right)^{16}$

Just like when before the variable terms may have a Coefficient

Multiple Choice

Simplify the exponential expression. $\left(3^2a^4\right)^5$

$3^{10}a^9$

$3^{10}a^{20}$

$3^7a^9$

$3^7a^{20}$

Multiple Choice

Simplify. $\left(2cd^2\right)^4$

$2^4c^4d^6$

$2^4c^4d^8$

Multiple Choice

$\left(3n^4\right)^3$

$9n^{12}$

$9n^7$

$27n^7$

$27n^{12}$

Multiple Choice

Simplify the following expression:

(3x³y⁵)⁴

3x¹²y²⁰

81x¹²y²⁰

12x¹²y²⁰

81x⁷y⁹

Let's mix them up the Laws!

Multiple Choice

Simplify.

-(2xy)(4x²y⁵)²

-32x⁵y¹¹

32x⁵y¹¹

-32x⁵y⁸

-16x⁵y¹¹

Multiple Choice

Simplify.

3(-2x³y⁴)⁴

48x¹²y¹⁶

-48x¹²y¹⁶

-24x¹²y¹⁶

-24x⁷y⁸

Multiple Choice

Simplify $\left(\frac{6c}{d}\right)^3$

$\frac{6c^3}{d^3}$

$\frac{216c^3}{d^3}$

$\frac{36c^3}{d^3}$

$\frac{216c^3}{d}$

Multiple Choice

Simplify $\left(\frac{cd^2}{d}\right)^5$

$\frac{cd^{10}}{d^{ }}$

$\frac{c^5d^{10}}{d^{ }}$

$c^5d^{10}$

$c^5d^5$

LAWS OF EXPONENTS

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