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Level 47

Exponents & Roots


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5-base
5⁴
factor
A number that divides evenly into another number. 3 is a factor of 15 (look at the chart!)
Scientific notation
where a number is written into 2 parts first just the digits (with decimal point after first digit) followed by ×10 to a power
Evaluate
To find the value of a mathematical expression.
expression
A mathematical phrase without an equal sign.
product
the answer to a multiplication problem
quotient
the answer to a division problem
a⁵
a² × a³
z³×z³×z⁵
z¹¹
2⁷/ 2²
2⁴ × 2³/ 2²
x³/ x²
b⁴
b⁷÷ b³
6¹³/ 6⁵
6⁴· 6⁹ / 6² ·6³
(7y²)²
49y⁴
(2k6)⁵
32k³⁰
(-w³)⁵
-w¹⁵
(-5)⁴
(-5) (-5) (-5) (-5)
3·3·5·q·q·q
3²·5·q³
(1/3)⁴
1/81
(-9)⁴
6561
2·2·2·5·5·11
Interstate 70 stretches 2³·5²·11 miles across the USA. About how many miles long is Interstate 70?
g⁵− h³
g⁵− h³ g=2 and h =7
3² =9, 3¹=3
As the exponents decrease, the value is divided by 3
2³ =8
Now use a similar pattern to predict the value of 2⁻¹.
7-¹
1/7¹
w-¹³
1/w¹³
1/12⁴
12−⁴
1/125
You have to think 5 to the what equals 125?
2−⁷
2−³ · 2−⁴
(3a¹)(a−³)
(3a) (a−³)
⁻3¹/ 3⁻⁵
3(exponent 4)
Evaluate 3⁻⁴
1/3 (exponent 4)
⁻6², 6⁻¹, 6°,6¹, 6³
6³, 6°, 6−¹, 6−², 6¹
10
The number before the decimal point must be between 1 and _______________.
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself
Right
a positive exponent means the original decimal needs to move to the _______________________
left
- subraction
7325
7.325 × 10³
.0046
4.6 × 10⁻³
Positive
Counting from the decimal point to the right makes the exponent ___________________________________________
Negative
Counting from the decimal point to the left makes the exponent ___________________________________
34, 690
3.469 × 10⁴
.039
3.9 × 10−²
529
(3.9×10²) (2.3×10³)
What key do you use for inputting an exponent?
2nd function-> drg->sci-> enter (=)
How do you change your calculator to scientific notation mode?
2nd function->drg-> fal->enter (=)
How do you change your calculator back to the drg mode?
Base
the number that is written with an exponent
Squared
A number with an exponent of 2 is often said to be
cubed
A number with an exponent of 3 is often said to be
itself
Any number with an exponent of 1 is equal to
1
Any number with an exponent of 0 is equal to
1
1 to any power is equal to
0
0 to any power is equal to
5
5^1 =
1
3^0 =
1
1^4 =
0
0^5 =
1 divided by that number with a positive exponent
Any number with a negative exponent is equal to
2
What number multiplied by itself is equal to 4? Well, 2. x 2 = 4, so the answer is
Because 4 multiplied by itself equals 16.
What number multiplied by itself is equal to 16? The answer is 4. Why?
Square Root
when multiplying a number by itself to get a square number
radical sign
The symbol for the square root of a number is the, a sign placed in front of an expression to denote that a root is to be extracted.
9 (3^2 = 9)
The square of 3 is
3
The square root of 9 is
0
The square root of zero is
The solution exists, but not in the real number system.
Don't bother trying to find the square root of a negative number.
Calculator square-root key
To find the square root of any number, simply key in the number (the radicand) and press the
cube root
the number that is multiplied by itself three times
The symbol for the cube root of a number is
the radical sign with a little 3 that indicates the cube root:
0
The cube root of zero is
Negative number
a number less than zero
Not
negative cube roots are okay ... negative square roots are
Same base
Numbers with exponents can be directly multiplied or divided only when they have the
Step 1: Add the exponents
To multiply powers that have the same base:
To divide powers that have the same base:
Step 1. Subtract the exponents (divisor from dividend) Step 2. Use the common base
Subtract the exponent
To divide powers that have the same base; what do you do to the divisor from the exponent of the dividend?
To multiply or divide exponent terms that do not have the same base:
Step 1. Evaluate each term with normal decimal notation. Step 2. Complete the multiplication or division.
There are no special rules for adding and subtracting numbers that are written with exponents.
Each number must first be converted to its ordinary decimal form, then complete the addition/subtraction operation.
To add or subtract numbers written with exponents:
Step 1. Rewrite each number with normal decimal notation. Step 2. Complete the multiplication or division.
a fractional decimal — a value less than 1.
A negative exponent does not mean the decimal value is negative. It means the decimal value is
10^1
10, or 1 with the decimal point moved one place to the right
10^2
100, or 1 with the decimal point moved two places to the right
When the exponent of a power-of-10 expression is a negative integer:
10^-1 = 0.1, or 1 with the decimal point moved one place to the left.
10^-1
= 0.1, or 1 with the decimal point moved one place to the left.
10^-2
= 0.01, or 1 with the decimal point moved two places to the left.
10^-18
represents 1 preceded by 17 zeros and a decimal point.
2 x 10^9
A very large number such as 2,000,000,000 can be written with scientific notation as
6.74 x 10^-7
A very small number such as 0.000000674 can be written with scientific notation as
Coefficient
the decimal part
proper scientific
when this is exactly one digit (not including zero) to the left of the decimal point. This sometimes called the normalized form.
Step 2. to Rewriting Decimal Values in Scientific Notation
Use a power-of-10 expression to restore the value of the original decimal.
Scientific notation requires there to be only
one digit to the left of the decimal point
adjust the value of the coefficient
When working with scientific notation, you are often required to change the location of the decimal point in the coefficient, but when you move the decimal point, you must