What happens when you raise a positive proper fraction to a power?

The value of the fraction decreases

Decimals between 0 and 1 increase in value when raised to a higher power

TRUE or FALSE?

FALSE - they DECREASE in value

You can distribute the powers in a compound base if there is a sum of two numbers inside the parenthesis

TRUE or FALSE

FALSE - you can only do this with multiplication inside parenthesis

You can't distribute the powers in a compound base if the base is a product of two numbers inside the parenthesis

TRUE or FALSE

FALSE - you can distribute the exponent to each number in the base, or you can multiply the base together and then raise it to the exponent

RULE: When multiplying two terms with the same base, ______ exponents by _____

combine, adding

combine, subtracting

combine, multiplying

Reciprocal

Negative exponents essentially mean...

Divide by the base that certain number of times

(3/4)^-3 = ?

(4/3)³

1/4^-2 = ? = 4² = 16

1/ 1/4²

(-2)³ = ? = - 1/8

1/(-2)³

(3/4)^-3 = ? = 64/27

(4/3)³

25^3/2 = ?

sq.rt (25³⁾

x^a..x^b = ?

x^a+b

a^x.b^x = ?

 (ab)^x

e.g.  2²3² = 2*2*3*3 = 4*9 = (6)²= 36

x^a/x^b =

 x^(a-b)

(a/b) ^x = ?

a^x / b^x

(a^x) ^y = ? = (a^y)^x 

a^xy

x ^{- a} = ?

1/x^a

x^a/b= b√x^a  = ?

x^a/b= ? = (b√x)^a

b√x^a  

x^a + x^a + x^a = ?

 3x^a

3^x + 3^x + 3^x = ? = ?

 3.3^x = 3^{x + 1}

3⁴ + 3⁴ + 3⁴  = ? = ? = ?

 3.3⁴ = 3¹.3⁴ = 3⁵

Simplify or Factor 7⁴ + 7⁶

Cannot be simplified!

Factor = 7⁴(7²+1) = 7⁴(50)

Simplify 12⁷ - 3⁷

Cannot simplify!

You can't factor terms when the exponent is the same and the terms contain something in common in the base

TRUE or FALSE?

FALSE - you can!

e.g. 3⁴ + 12⁴ can be factored because 12⁴ = (2 x 3 x 3)⁴

What's (0.04)³ ? Solve 3 ways...

4³/100³ = 64/1000000 = 64 x 10^-6 = 0.000064

or

(4 x 10^-2)³ = 4 x 10^-6 = 0.000064

or

0.000064 (i.e. 4x4=64, with 3 times the original # decimal places in the original decimal)