Rational Exponents & Radicals (Laws of Exponents Review)

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Rational Exponents
and
Radicals (Lesson 4)


Review Lesson 3:
Laws of Exponents

TASK 1

Review the rules for exponents & write on the notecard, see the next slide

Expressions with Exponents

Multiple Choice

Simplify the expression $$\left(x^5\right)\left(x^7\right)$$

• $$x^{35}$$

• $$x^{-2}$$

• $$x^{12}$$

• $$x^2$$

Multiple Choice

$$x^3\ \times x^8$$

• x¹¹

• x²⁴

• x⁵

Multiple Choice

$$b^3\cdot b^4\cdot b^7\cdot b$$  

• $$b^{15}$$  

• $$b^{14}$$  

• $$b^{84}$$  

• $$b^{49}$$  

Multiple Choice

4⁷/4²

• 4x⁵

• 4x⁹

• 1x⁵

• 1x⁹

Multiple Choice

(4²)³

• 16³

• 4⁵

• 4⁶

• 4¹

Multiple Choice

(a³b)⁴

• a¹²b⁴
• a⁷b⁵
• a³b⁴
• ab⁸

Multiple Choice

Simplify

• $$\frac{1}{8}$$  

• -16

• $$\frac{1}{16}$$  

• 16

Multiple Choice

Simplify.

• y¹⁵
• y⁵
• y²
• 2y⁵

Multiple Choice

Simplify.   $$\frac{x^{-4}}{x^3}$$  

• $$\frac{1}{x^7}$$  

• $$x^7$$  

• $$\frac{x^3}{x^4}$$  

First lets review exponents and square root

Multiple Choice

Write each product using an exponent. 
4 x 4 x 4 x 4 x 4 

• 4⁵

• 5⁴

• 4⁶

• 4⁶

Multiple Choice

√16 is equal to-

• -16

• 4

• 256

• 8

Rational Exponents

• The numerator (top of the fraction) is the exponent

• Hint: exponent goes at the TOP of the number

• The denominator (bottom of the fraction) is the root

• Hint: the roots are at the BOTTOM of the tree.

Multiple Choice

Write in exponential form
√x⁵

• X¹∕ ⁵

• X ²⁄⁵

• X⁵⁄ ²

• X⁵

Multiple Choice

Write the expression in radical form.

x^3/4

• ∜x³

• ∛x⁴

• x^.75

• √x²

Multiple Choice

Write with a rational exponent.

• 7³

• 7

• 7^3/4

• 7^4/3

Multiple Choice

Write with a rational exponent.

HINT: what exponent is at the 2? It is "invisible"

• 2^1/6

• 64

• 6^1/2

• 2⁶

Multiple Choice

Write with a rational exponent.

HINT: what root is it? It is "invisible"

• 216

• 6^1/2

• 6²

• 6^3/2

Multiple Choice

Write the expression in radical form.

x^7/2

• √x⁷

• 7√x²

• 7x²

• ∛x⁷

Multiple Choice

Write with a rational exponent.

HINT: both are invisible.

• 7²

• 7^1/2

• 7^-2

• 7^-1/2

Multiple Choice

∜m³ is the same as which answer?

• m^3/4

• m¹²

• m^4/3

• m⁷

Multiple Choice

Write as a radical.

• a

• b

• c

• d

Multiple Choice

Rewrite in radical form.

• A

• B

• C

• D

Multiple Choice

Write the following expression in exponential form:

• a.)

• b.)

• c.)

• d.)