Madi'sMagnificantMathPage!


 * "I AM NOT AFRAID OF EXPONENTS, I AM SMARTER THAN EXPONENTS!!"**

**Vocabulary**:
1. Exponent - The number that indicates how many times you multiply that factor. 2. Base - Indicates what number you multiply to get the answer. 3. Standard Form - The answer. 4. Expanded Notation - A way of writing a number to show what values are in which places. 5.Exponential Form - When the number is written as a "power" with a base + an exponent. 6. Factored Form - Written showing all the factors.

**REMINDERS** - Any number to the power or zero equals 1! - Anything there is a negative exponent you "flip" the base

When multiplying exponents with common bases, keep the base and add the exponents.
Example: (5x⁴ y³)⁶ • (5x⁴y³)⁹ (5x⁴y³)⁶+⁹ (5x⁴y³)¹⁵

When dividing exponents with a common base, keep the base and subtract the exponents.
Example: (a⁴b¯¹c³)÷(a¯¹¹b²c⁵) a⁴--¹¹ = a¹⁵ b-¹-² = b-³ c³-⁵ = c-² = a¹⁵b-³c-²  REMINDERS - The base is the only thing attached to the exponent - Odd exponents are negative and even exponents are positive - Odd exponents multiplied by a negative number will be negative**
 * - When rewriting with positive exponents only move the negative things

=**__3.4 Power of a Power Property __**=


When solving questions with two or more exponents and a set of parentheses on a number or variable you use the power of a power property. The rule is keep the base and multiply the exponents Examples: 1. (8⁵)³ =8¹⁵ 2. __(8x⁵y⁶)³__ z⁴ = __8³x¹⁵y¹⁸__ z¹² **REMINDERS** - Remember to distribute when needed! I did not get a lollipop:(

__3.5 Calculations with Exponents(BEDMAS)__
B- Brackets E- Exponents D- Division M- Multiplication A- Addition S- Subtraction

<span style="color: rgb(146,169,61);">Examples: 1. 5³+5² 2. 3-¹+3-²

125 + 25 = __1__ + __1__
=150 3¹ 3² = __1×3__ + __1__

3×3 9
= __3__ + __1__ 9 9 = __4__ 9

<span style="color: rgb(204,25,193);">Rules:
<span style="color: rgb(9,155,159);">- If you move the decimal to the left you add to the exponent. - If you move the decimal to the right you subtract from the exponent - You __CANNOT__ have 2 or more digits to the left of the decimal. - The number to the left of the decimal has to be in between 1-9. <span style="color: rgb(9,155,159);">- Negative exponents = smaller - Positive exponents = bigger <span style="color: rgb(128,20,83);">Example:  ** 1. 87 000 000 000 = 8.7x10¹⁰ 2.724 000 000 = 7.42x10⁸ 3.-276 300 000 000 000 = -2.763x10¹⁴
 * <span style="color: rgb(0,128,0);">

<span style="color: rgb(165,39,123);">__3.7 Multiplication and Division Using Scientific Notation__
<span style="color: rgb(15,95,133);">__How to?__ 1.Put into scientific notation 2.Put numbers together and multiply or divide according to the question 3.Put powers of 10 together and add or subtract exponents according to question 4.Answer(Adjust decimal if needed!)

Examples: __Multiplication__ __Division__ __Multi/Divid..__ 13000x340000 2250000÷2500 __36000x0.0074__ (1.3x10⁴) (3.4x10⁵) (2.25÷2.5)x(10⁶÷10³) 4000 (1.3x3.4) (10⁴x10⁵) (0.9)x(10³) <--- move the decimal 4.42x10⁹ 9.0 x 10³-¹ __(3.6x10⁴)x(7.4x10-³)__ 9.0 x 10² (4.0x10³)

__(3.6x7.4__) x __(10⁴x10-³)__ 4 10³

= 66.66x10-²