Indices Flashcards
When multiplying terms with the same base with powers, what do you do?
Add the powers together.
3^2 x 3^3 = 3^5
When dividing terms with the same base with powers, what do you do?
Subtract the powers.
27^5 ÷ 27^3 = 27^2
When raising a term with a power to another power, what do you do?
Multiply the powers.
(4^3)^2 = 4^3x2 = 4^6
When raising a product of terms to a power, what do you do?
Raise each term to that power.
(3z)^4 = 3^4 z^4 = 81z^4
When raising a quotient of terms to a power, what do you do?
Raise each term to that power.
(4/7)^2 = 4^2/7^2 = 16/49
When a number is raised to the power of zero, what happens?
Every number raised to the power of zero is equal to 1.
7^0 = 1
When a number is raised to a negative power, what happens?
A fraction is made with a numerator of 1.
3^-3 = 1/3^-3 = 1/27
When a problem is raised to the the power of -1, what happens?
The problems reciprocal is given.
(2/3)^-1 = 3/2
When a number is raised to the power of -n, what hapens.
It’s reciprocal is given.
(3/4)^-n = (4/3)^n = 4^n/3^n
Solve (8^4)^3
(8^4)^3 = 4^3x4 =4^12
Solve 9^0
9^0 = 1
Solve 2^5 x 2^3
2^5 x 2^3 = 2^5x3 = 2^15
Solve 14^12 ÷ 14^3
14^12 ÷ 14^3 = 14^12-3 = 14^9
Solve (2/6)^h
(2/6)^h = (6/2)^h = 6^h/2^h
Solve (2/15)^2
(2/15)^2 = 2^2/15^2 = 4/225
What is a significant figure?
A significant figure is the first non-zero digit in a number.
What do significant figures do?
Significant figures are a way of including the most relevant digits in a number.
How many significant figures are in 6557.0890?
7 significant figures (the zero is used as a placeholder for the other numbers).
How many significant figures are in 8.20
2 significant figures (8 and 2).
How many significant figures are in 108.225060
8 significant figures (the zero is used as a placeholder for the other numbers).
How many significant figures are in 557809.08892
11 significant figures (the zero is used as a placeholder for the other numbers).
Explain scientific notation.
Numbers are expressed in the equation:
m x 10^n
m is a number between 1 and 10.
n is an integer.
Write 900 in scientific notation.
9 x 10^2.
Write 1200 in scientific notation.
1.2 x 10^3.
Write 10,000 in scientific notation.
10 x 10^3.
Write 4,900,000 in scientific notation.
4.9 x 10^6.
Write 9,800,000,000 in scientific notation.
9.8 x 10^9.
