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Section P.2

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Section P.2

Exponents and Radicals

- An exponent is the power p in an expression ap.
52

- The number 5 is the base.
- The number 2 is the exponent.
- The exponent is an instruction that tells us how many times to use the base in a multiplication.

(-5)2 = -52?

(-5)(-5) = -(5)(5)

25 = -25

43

-34

(-2)5

(-3/4)2

=(4)(4)(4) = 64

=(-)(3)(3)(3)(3) = -81

=(-2)(-2)(-2)(-2)(-2)= -32

=(-3/4)(-3/4) = (9/16)

Which of these will be negative?

3235

= (3)(3)(3)(3)(3)(3)(3)

= 37

Note 2+5=7

- If a is any real number and r and s are integers, then

To multiply two expressions with the same base, add exponents and use the common base.

Notice that

5 – 3 = 2

- If a is any real number and r and s are integers, then

To divide like bases subtract the exponents.

Notice that

3 – 5 = -2

- If nis a positive integer, then

Notice that: Negative Exponents do not indicate negative numbers.

Negative exponents do indicate Reciprocals.

Notice that exponent does not touch the 3.

Undefined

STOP

Zeros are not allowed in the denominator. So 00 is undefined.

- If a and b are any real number and r is an integer, then

Distribute the exponent.

(32)3

= ((3)(3))1((3)(3))1((3)(3))1

= 36

Note 3(2)=6

- If a is any real number and r and s are integers, then

A power raised to another power is the base raised to the product of the powers.

One base, two exponents… multiply the exponents.

Let a and b be real numbers and let n ≥ 2 be a positive integer. If

a = bn

then b is the nth root of a.

If n = 2, the root is a square root.

If n = 3, the root is a cube root.

- The nth root of a product is the product of nth roots

- The nth root of a quotient is the quotient of the nth roots

10

4

8

3

3

2

A radical expression is in simplified form if

1. All possible factors have been removed from the radical. None of the factors of the radicand can be written in powers greater than or equal to the index.

2. There are no radicals in the denominator.

3. The index of the radical is reduced.

This will always be a perfect square.

Often you will not need to write this step.

5

Must have 3 of a kind

Must have 3 of a kind

3

2

- Page 21
- #9 – 42 multiples of 3 (a’s only),
- 55 – 63 odd (a’s only)
- 72 – 84 Multiples of 3 (a’s only)
- 95 – 99 odd (a’s only)