Exponent Rules & Simplifying Radical Expressions Review

Exponent Rules & Simplifying Radical Expressions Review

By Mr. Foreman

Draw

Let's get abstract before we do math, draw Mr. Foreman as a giraffe playing a guitar (honestly, I'm just doing this to see how this shows up on my end)

When you have two expressions you are multiplying together, exponents add!

​

MULTIPLYING EXPONENTS -> ADDING!​

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

Multiple Choice

$$m^2\cdot m^6\cdot m=$$  

• $$m^8$$  

• $$m^{12}$$  

• $$m^4$$  

• $$m^9$$  

Multiple Choice

$$x^{-3}\cdot x^7\cdot x^2$$  =

• $$x^6$$  

• $$x^{12}$$  

• $$x^{-42}$$  

• $$x^{-12}$$  

Multiple Choice

Simplify: $$3n^5\cdot5n^{10}$$  

• $$15n^5$$  

• $$8n^{15}$$  

• $$15n^{50}$$  

• $$15n^{15}$$  

Multiple Choice

Simplify: $$\left(3k^5\right)\left(-2k^3\right)$$  

• $$6k^8$$  

• $$-6k^{15}$$  

• $$6k^{15}$$  

• $$-6k^8$$  

Multiple Choice

Simplify   (2m⁴)(5m²)

• 10m⁶
• 10m⁸
• 7m⁶
• 7m⁸

When you have two expressions you are dividing together, exponents subtract!

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DIVIDING EXPONENTS

-> SUBTRACTING!​

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

Simplify: $$\frac{12x^5y^4}{2x^9y}$$  

• $$6x^{-4}y^3$$  

• $$\frac{6y^3}{x^4}$$  

• $$\frac{12y^3}{2x^4}$$  

• $$\frac{6x^{-4}}{y^3}$$  

Multiple Choice

$$\left(\frac{x^4}{x^2}\right)^3$$   Click on the play button if you need a hint

• $$x^8$$  

• $$x^6$$  

• $$x^3$$  

• $$x^9$$  

Multiple Choice

• 3ab⁸c³

• 2ab⁸c¹¹

Multiple Choice

Anything to the 0 power is 1 so essentially the z^0 will go away in the numerator!

• 2x²z⁴

• 3x²y⁵z⁴

When you have an expression that you are raising to a whole other power, exponents multiply!

​

RAISING EXPONENTS TO AN EXPONENT

-> MULTIPLYING

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

Simplify: $$\left(2m\right)^5$$  

• $$10m^5$$  

• $$32m^5$$  

• $$25m^5$$  

• $$\frac{1}{2m^5}$$  

Multiple Choice

Simplify: $$\left(3x^5\right)^6$$  

• $$18x^{30}$$  

• $$729x^{11}$$  

• $$3^6x^{30}$$  

• $$729x^{30}$$  

Multiple Choice

(5x²y²)³

• 125x⁶y⁶
• 15x⁶y⁶
• 8x⁵y⁵
• 15x⁵y⁵

Multiple Choice

Simplify: $$\left(4y\right)^{-3}$$  

• $$\frac{1}{64y^3}$$  

• $$64y^{-3}$$  

• $$-12y^{-3}$$  

• $$\frac{64}{y^3}$$  

Multiple Choice

• $$\frac{16x^{16}z^{32}}{y^{28}}$$

• $$\frac{-16x^{16}z^{32}}{y^{28}}$$

• $$\frac{x^{16}z^{32}}{16y^{28}}$$

• $$-8x^{-8}y^3z^{-12}$$

Multiple Choice

Simplify: $$\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$$  

HSimplify the left chunk first, then multiply to simplify further!

• $$16a^8b^9c^9$$  

• $$8a^8b^9c^9$$  

• $$8a^6b^5c^6$$  

• $$16a^5b^5c^6$$  

Multiple Choice

HINT: Anything to the 0 power is always...

• -15x²yz⁴
• 1

Check this video out if you need a refresher on how Square Roots work (especially when ​you multiply square roots together!)

Simplifying RADICALS

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

Simplify the following radical: √300

• 3√10
• 2√150
• 100√3
• 10√3

Multiple Choice

Simplify 4√75

• 4√5
• 12√5
• 20√3
• 7√3

Multiple Choice

Simplify:

• A
• B
• C
• D

Multiple Choice

Simplify:
6√2 ⋅5√14

• 32√7
• 60√7
• 2√7
• 30√7

Multiple Choice

Simplify  -2√10 ⋅ 3√20

• -60√2
• 10√2
• √30
• -6√200

Multiple Choice

Simplify:
√6 ⋅√6

• √36
• 2√3
• 12
• 6

​Remember, it's just like combining like terms (SIMPLIFY THE RADICALS AND COMBINE WHAT IS ALIKE!)

ADDING & SUBTRACTING RADICALS

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

• 8√6
• 8√12
• 12√6
• 12√12

Multiple Choice

Add:  4√7 - 10 √7 + 7√7

• -6√7
• 14√7
• -3√14
• √7

Multiple Choice

 Simplify:   2√40 - 3√10 

• 5√10
• √10
• -√30

Multiple Choice

√98 + 5√2

• 8√3
• 12√2
• 7√2
• 7√3

Multiple Choice

Simplify 
-2√2-3√8-√5

•  -8√2-√5
• -8√2-√9
• -14√3-√7
• -2√4-√3

​For these, you must first multiply by whatever radical is in the denominator (if there is no radical in the denominator, then just work it out as usual!) The process of multiplying by the radical in the denominator is called "Rationalizing" the denominator!

DIVIDING RADICALS

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

Simplify:

• √5
• (√14)/2
• √7
• Cannot be simplified

Multiple Choice

Simplify:

• 2
• 4√3
• 2√3
• 4

Multiple Choice

Simplify:

HINT: Multiply the numerator & denominator just by √9!

• A
• B
• C
• D

Multiple Choice

Rationalize the denominator: $$\frac{\sqrt{5}}{2\sqrt{3}}$$  

• $$\frac{\sqrt{15}}{6}$$  

• $$\frac{\sqrt{15}}{18}$$  

• $$\frac{5\sqrt{3}}{6}$$  

• $$\frac{5\sqrt{3}}{18}$$  

Multiple Choice

Rationalize the denominator: $$\frac{2\sqrt{8}}{\sqrt{12}}$$  

• $$\frac{\sqrt{96}}{6}$$  

• $$\frac{2\sqrt{6}}{3}$$  

• $$\frac{2\sqrt{96}}{12}$$  

• $$\frac{4\sqrt{2}}{2\sqrt{3}}$$  

Higher order radicals are actually quite fun since you just look for how much to cancel out based on the index (or you could always just divide by the index and the remainder goes inside the radical!)

HIGHER ORDER RADICALS!

HERE IS A REFRESHER IF YOU NEED IT!

Multiple Choice

Simplify: √(28xy²)

• 2y√(7x)
• √(28xy²)
• y√(28x)
• 7x√(2y)

Multiple Choice

Simplify the radical expression: $$\sqrt{92a^2b^3}$$  

• $$23ab\sqrt{2b}$$  

• $$2ab\sqrt{23b}$$  

• $$4ab\sqrt{23b}$$  

• $$4a^2b^2\sqrt{23b}$$  

Multiple Choice

• yz⁶  ⋅ ∛xy²z²
• yz⁶  ⋅ ∛xyz
• y²z¹⁰ ⋅ ∛xy²z²
• y²z¹⁰ ⋅ ∛xy

Multiple Choice

Simplify the expression:

• 3y⁴∜5x³y³
• 9xy∜5xy³
• 121.5x^.75y^1.75
• 3y∜5x³y³

Multiple Choice

$$Simplify^{\ \ 4}\sqrt{fg^{12}h^{14}}$$  

• $$g^3h^{2\ \ 4}\sqrt{fh^4}$$  

• $$g^6h^{7\ }\sqrt{f}$$  

• $$g^3h^{3\ \ 4}\sqrt{fh^2}$$  

• $$fg^3h^{4\ \ 4}\sqrt{h^2}$$  

Multiple Choice

Simplify:

• 6x²
• 18x²

Multiple Choice

• A

• B

• C

• D

Poll

Did you like this sort of assignment? It took me a while to put it together so I genuinely want to see if it's something you think others would enjoy.

For those who are uncertain which to pick

Yeah Man means "Yes"

No Man means "No"

Man with Airpods in staring off in the distance means "Indifferent"

Shrek Wazowski means . . . well Shrek Wazowski, there's not much more to explain there.