Math Study Guide: Topic 9: Exponents and Square Roots (pages 45-48)

Question 1

What is an “exponent?”

(and what is another word for “exponent?”)

Answer 1

An “exponent” (or “power”) is the number of times a number is multiplied by itself.

X³ = X times X times X

Question 2

How do multiply exponents?

Answer 2

Add the powers:

X³ x X² = X⁵

Question 3

How do you divide exponents?

Answer 3

Subtract the powers:

X⁸ ÷ X³ = X⁵

Question 4

How do you raise one power to another?

Answer 4

Multiply the powers:

(X⁴)³ = X⁴ x X⁴ x X⁴ = X¹²

Question 5

How do you simplify X³ x Y² ?

Answer 5

You can’t, because you must have the same base (X or Y)

Question 6

Can you add X³ + X² together?

Answer 6

No, because both the base and power must be the same.

But you can add the
“coefficients” (the number in front of the base)

Question 7

Can you add X³ + X³ ?

Answer 7

Yes

X³ + X³ = 2X³

Question 8

What is Y⁵ + 3Y⁵ ?

Answer 8

Y⁵ + 3Y⁵ = 4Y⁵

Question 9

What is another way of writing X³ + X² differently?

Answer 9

By “factoring” out X², as in:

X³ + X² = X²(X + 1)

Question 10

What is X¹ ?

Answer 10

X

Question 11

What is X⁰ ?

Answer 11

1

Question 12

What is 1^x ?

Answer 12

1

Question 13

What is 0^x ?

Answer 13

0

Question 14

What is X^-2 ?

Answer 14

1/X²

Question 15

What is X^½ ?

Answer 15

√X (the square root of X)

Question 16

What is the “square root” of a number?

Answer 16

The “square root” of a number is the value that, when multiplied times itself, gives the original number.

Example: The square root of 9 is 3 since 3 x 3 = 9

Question 17

What are numbers like 4, 9, 16, 25, etc. called, and why?

Answer 17

“Perfect squares” because their square root is a whole number.

Question 18

How do you write the square root of numbers such as 7?

Answer 18

The square root of 7 is simply written as √7 because 7 does have a whole number as a square root.

Question 19

Can you multiply square roots?

Answer 19

Yes

Example: √3 x √5 = √15

Question 20

Can you divide square roots?

Answer 20

Yes

Example: √30 ÷ √5 = √6

Question 21

Can you add or subtract square roots?

Answer 21

Only when the number underneath the square root sign is the same:

√5 ± √6 ≠ √11

but

√5 + √5 = 2√5

Question 22

When (and how) can you simplify a square root?

Answer 22

You can simplify a square root when a perfect square can divide into the number inside:

Example 1:
to simplify √18, change it to √9 x √2 = 3√2

Example 2:
to simplify 6/√3, you can multiply 6/√3 by √3/√3 =

6√3 /3 =
2√3