Math Study Guide: Topic 9: Exponents and Square Roots (pages 45-48) Flashcards
What is an “exponent?”
(and what is another word for “exponent?”)
An “exponent” (or “power”) is the number of times a number is multiplied by itself.
X3 = X times X times X
How do multiply exponents?
Add the powers:
X3 x X2 = X5
How do you divide exponents?
Subtract the powers:
X8 ÷ X3 = X5
How do you raise one power to another?
Multiply the powers:
(X4)3 = X4 x X4 x X4 = X12
How do you simplify X3 x Y2 ?
You can’t, because you must have the same base (X or Y)
Can you add X3 + X2 together?
No, because both the base and power must be the same.
But you can add the
“coefficients” (the number in front of the base)
Can you add X3 + X3 ?
Yes
X3 + X3 = 2X3
What is Y5 + 3Y5 ?
Y5 + 3Y5 = 4Y5
What is another way of writing X3 + X2 differently?
By “factoring” out X2, as in:
X3 + X2 = X2(X + 1)
What is X1 ?
X
What is X0 ?
1
What is 1x ?
1
What is 0x ?
0
What is X-2 ?
1/X2
What is X½ ?
√X (the square root of X)
What is the “square root” of a number?
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
What are numbers like 4, 9, 16, 25, etc. called, and why?
“Perfect squares” because their square root is a whole number.
How do you write the square root of numbers such as 7?
The square root of 7 is simply written as √7 because 7 does have a whole number as a square root.
Can you multiply square roots?
Yes
Example: √3 x √5 = √15
Can you divide square roots?
Yes
Example: √30 ÷ √5 = √6
Can you add or subtract square roots?
Only when the number underneath the square root sign is the same:
√5 ± √6 ≠ √11
but
√5 + √5 = 2√5
When (and how) can you simplify a square root?
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
