Cube and Square roots, with zero power and negative exponents

Exponents

Exponents represent repeated multiplication.

​Remember what an exponent does.

​When you have an exponent, the exponent tells you how much to multiply the number by itself.

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​This is the visual representation of 3 squared.

• ​When you square a number you multiply it by itself. The answer you get is called a perfect square. All perfect squares can be represented using the square model shown here.

​List of the most commonly used perfect squares.

​In your notes you need this list of the most common perfect squares and perfect triples. It is in your best interest to have these memorized before you go to algebra.

Squares and Square Roots

We can also invert cubes.

Cubes and Cube Roots

We could use the cube root symbol, which is a radical with a little three in the index place.

Multiple Choice

Which of the following represents 4² ?

Multiple Choice

To find the square root of a number, you must divide it by 2.

• True

• False

Multiple Choice

When you square a number you multiply that number by ____________

• 4

• 2

• itself

• 10

Multiple Choice

What does this symbol represent?

• square root/radical symbol

• divide by 2

• cube root

• greater than or less than

Multiple Select

What number represents the base?

• 3

• 5

• 15

• 125

Multiple Choice

What number is the exponent?

• 3

• 5

• 15

• 125

Multiple Select

Select ALL of the following that are equivalent to 5×5×5

• five cubed

• five squared

• 5³

• 3⁵

• 125

Multiple Choice

Square root is the inverse of ____________.

• Cube Roots

• Squaring a number

• Multiplication

• Absolute Value

Multiple Select

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

• $$14$$  

• $$7\times7$$  

• $$7\times2$$  

• $$49$$  

• $$7+2$$  

Poll

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

• Yes

• No

Multiple Choice

∛8

• 2

• 4

• 1

• 64

Multiple Choice

9³

• 689

• 709

• 729

• 749

Fill in the Blank

3³=

Multiple Choice

$$\sqrt[3]{27}$$  

• 3

• 4

• 327

Multiple Select

What is the difference in $$\sqrt[]{64}$$  and $$\sqrt[3]{64}$$ ?

Choose all that apply.

• One is a square root and one is a cube root.

• They are the same thing

• The answers are $$\sqrt[]{64}=8$$   and $$\sqrt[3]{64\ }=4$$  

Multiple Choice

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

• Yes

• No

​Remember your rule for multiplying.

Multiple Choice

$$\left(-7\right)^2$$  

• -14

• 14

• -49

• 49

Multiple Choice

What is $$\left(-9\right)^2$$  

• 18

• -18

• 81

• -81

Multiple Choice

$$-6^2$$  = ?

• 12

• -12

• -36

• 36

Fill in the Blank

4³=

Multiple Choice

∛64

• 4

• 5

• 6

• 3

Multiple Choice

$$\sqrt[3]{125}$$  

• 3125

• 5

• 25

Multiple Choice

$$\sqrt[3]{1000}$$  

• 10

• 100

• 125

Multiple Choice

$$7\sqrt{4}$$  

• 28

• 14

• 11

• 9

Multiple Choice

Write in exponential form: 3 x 3 x 3 x 3

• 3 x 4

• 3⁴

• 81

• 3²

Multiple Choice

$$7^2-3$$  

• 17

• 11

• 52

• 46

Multiple Choice

3+ $$\sqrt[]{49}$$  

• 49

• 52

• 10

• 70

Multiple Choice

$$\sqrt{81}-\sqrt{16}$$  

• 5

• 13

• 1

• 8

Multiple Choice

$$\left(-15\right)^2$$  +10

• 40

• 225

• 2250

• 235

Open Ended

Tate is planning to put a square garden with an area of 289 square feet in his back yard. What will be the length of each side of the garden?

Type your final answer.

Multiple Choice

Mr. Jarowski is hanging a square picture frame that has ab area of 169 cm². Find the side length of the frame.

• 12 cm

• 13 cm

• 13 in

• 16 cm

Multiple Choice

Isaiah is creating a Spongebob poster and the side is 17 inches. What is the area of the Spongebob?

• 17

• 289

• 300

• 298

Multiple Choice

A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is each side of the portrait?

• 16

• 13

• 14

• 15

Multiple Choice

Len is baking a square cake for his friend’s wedding. When served to the guests, the cake will be cut into square pieces 1 inch on a side. The cake should be large enough so that each of the 121 guests gets one piece. How long should each side of the cake be?

• 7

• 12

• 11

• 15

Multiple Choice

Rosy wants a large picture window put in the living room of her new house. The window is to be square with an area of 49 square feet. How long should each side of the window be?

• 6

• 4.9

• 7

• 5

Multiple Choice

Cara has 196 marbles that she is using to make a square formation. How many marbles should be in each row?

• 13

• 16

• 12

• 14

Zero Exponents

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

Negative Exponents

Negative exponents means the reciprocal of the positive power.