Square and Cube Roots

Square Root and Cube Root

By Kevvin Hankins

Exponents, Squares, Square Roots, Cubes, and Cube Roots

Exponents

Exponents represent repeated multiplication. The exponent will only effect the term it is directly touching.

For example;

-4⁴ = - ( 4 x 4 x 4 x 4)

notice it did not involve the (-)

(-3)⁵ = -3 x -3 x -3 x -3 x - 3

notice due to parentheses the (-) was included!!!

Poll

Is  $$8^3$$  the same thing as  $$8\times3$$  ?

• Yes

• No

Poll

Is $$\left(-3\right)^2$$  the same thing as  $$-3^2$$  ?

• Yes

• No

Multiple Select

Select all the expressions that are equivalent to $$7^2$$ .

• $$14$$  

• $$7\times7$$  

• $$7\times2$$  

• $$49$$  

• $$7+2$$  

Zero Exponents

Any non-zero number or term raised to the zero power is 1.

(3x - 5 + 7x + 8)⁰

= (10x + 3)⁰

=1

Any non-zero number raised to the power of 0 will always result in 1.

Multiple Choice

$$8^0=$$  

• 0

• 1

• x

• -x

Multiple Choice

$$x^0=$$  

• 0

• 1

• x

• -x

Negative Exponents

Negative exponents means the reciprocal of the positive power.

If we want to write an expression with all positive powers, we can change their location from numerator to denominator and vice versa.

Multiple Select

Select all the expressions that are equivalent to $$4^{-3}$$  .

• $$-12$$  

• $$\frac{1}{64}$$  

• $$-64$$  

• $$\frac{1}{4^3}$$  

• $$64$$  

Squares and Square Roots

Multiple Choice

$$\sqrt{64}=$$  

• $$32$$  

• $$4$$  

• $$8$$  

• $$64^2$$  

Cubes and Cube Roots

Multiple Choice

$$3^3=$$  

• $$9$$  

• $$27$$  

• $$6$$  

• $$12$$  

Multiple Choice

  $$\sqrt[3]{8}$$

• $$\frac{8}{3}$$  

• $$2$$  

• $$512$$  

• $$5$$  

Open Ended

Well done! Please write one question you still have about exponents, squares, or cubes!