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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

x¹

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