Exponent Rules
When like bases are being multiplied, add the exponents. What rule is this?
Product Rule
When adding and / or subtracting numbers written in scientific notation, what must be true about the exponents?
They must have the same exponents.
Classify √17 as rational or irrational.
Irrational, because it is not a perfect square.
The average distance of the Moon from Earth is about 384,000 kilometers. Write this number in scientific notation.
3.84 X 105
The radius of Earth is about 6.38 X 103. Write the distance in standard notation.
6,380
When like bases are being divided, subtract the exponents. What rule is this?
Quotient Rule
When multiplying numbers in scientific notation, you must _________ the coefficients and then follow the _____________ rule of exponents.
multiply
product
Order from greatest to least.
π /4, -2.5, -√5, and 0.5
π/4, 0.5, −√5, −2.5
Write the following in scientific notation.
276
2.76 X 102
Write the following in standard notation.
4.56 X 10-4
0.000456
Simplify the expression by using the Power Rule.
(53)5
515
When dividing numbers in scientific notation, you must _________ the coefficients and then follow the _____________ rule of exponents.
divide
quotient
Rational numbers can be written as a decimal that ______________ or _______________and it can also be written as a ________________. They must also make a _______________ square or cube.
terminates
repeats
fraction
perfect
Which exponent would be most appropriate when 0.0000389 in scientific notation?
-5
Write the following in standard notation.
.81 X 10-3
.00081
Simplify the expression using the Power of a Product Rule.
(22 x 25)3
221
What is the product of (3 x 104)(4 x 105) written in scientific notation?
1.2 x 1010
True or False. The list below contains all rational numbers. Justify your answer.
√16 √4 √36 √81 √49
True because they are all perfect squares.
4 x 4 = 16, 2 x 2 = 4, 6 x 6 = 36, 9 x 9 = 81,
7 x 7 = 49
Write the following in scientific notation:
0.00000676
6.67 X 10-6
A grain of sand has a mass of 3.0 X 10 -4 gram. Write the number in standard notation
0.0003
Simplify the expression using the Negative Exponent Rule.
4-6
1/46
What is the quotient of 40 x 108/ 8 x 102 in scientific notation.
5 x 106
What is 3√8? Justify your answer.
2. Because 2 x 2 x 2 = 8.
Write the following from least to greatest (give your answer in terms of A,B,C)
A) 3.25 X 106 , B) 5.32 X 105 , C) 2.35 X 105
C, B, A
The speed of light in over 2.99 x 108 m/s. Write the number in standard notation.
299,000,000 m/s