Arithmetic I
2^3 * 2^4
2^3 * 2^4 = 2^(3+4) = 2^7 = 128
7^0 + 4^2
7^0 + 4^2 = 1 + 16 = 17
x^4 * x^3
x^4 * x^3 = x^(4+3) = x^7
x^(-5)
x^(-5) = 1/x^5
A rectangle has an area of 804 cm2. Its length is 12 cm. What is its width?
67 cm
(5^7)/(5^4)
(5^7)/(5^4) = 5^(7-4) = 5^3 = 125
2^(-3)
2^(-3) = 1/(2^3) = 1/8'
a^9/a^5
a^9/a^5 = a^(9-5) = a^4
x^3/x^7
x^3/x^7 = x^(3-7) = x^(-4) = 1/x^4
Which figure of speech compares two unlike things using the words “like” or “as”?
Simile
(3^2)^3
(3^2)^3 = 3^(2*3) = 3^6 = 729
(2/3)^(-2)
(2/3)^(-2) = (3/2)^2 = 9/4
((m^3)^4)^5
((m^3)^4)^5 = m^(3*4*5) = m^60
((2a^3)/(b^2))^2
((2a^3)/(b^2))^2 = (2^2a^(3*2))/(b^(2*2)) = (4a^6)/(b^4)
A historical document was signed on July 4, 1776, declaring that the thirteen American colonies were independent from Great Britain. What is the name of this document?
The Declaration of Independence
(2^8 * 2^3)/(2^6)
= 2^(8+3-6) = 2^5 = 32
(4^(-2))/(2^(-6))
(4^(-2))/(2^(-6)) = ((2^2)^(-2))/(2^(-6)) = (2^(-4))/(2^(-6)) = 2^(-4-(-6)) = 2^2 = 4
(3x^2y^3)^2
(3x^2y^3)^2 = 3^2x^(2*2)y^(3*2) = 9x^4y^6
(6x^(-2)y^5)/(3x^3y^(-1))
(6x^(-2)y^5)/(3x^3y^(-1)) = 2x^(-2-3)y^(5-(-1)) = 2x^(-5)y^6 = (2y^6)/(x^5)
What is the atomic number of an element equal to?
The number of protons in the nucleus
(3^5 * 9^2)/(27^2)
(3^5 * 9^2)/(27^2)= (3^5 * (3^2)^2)/((3^3)^2) = 3^(5+4-6)= 3^3= 27
(8^3 * 4^(-2))/(2^(-1))
(8^3 * 4^(-2))/(2^(-1)) = ((2^3)^3 * (2^2)^(-2))/(2^(-1)) = 2^(9-4-(-1)) = 2^6 = 64
(12x^8y^5)/(3x^3y^2)
(12x^8y^5)/(3x^3y^2) = 4x^(8-3)y^(5-2) = 4x^5y^3
((3x^(-2)y^3)/(2x^4y^(-1)))^(-2)
(3x^(-2)y^3)/(2x^4y^(-1)) = (3/2)x^(-2-4)y^(3-(-1)) = ((3y^4)/(2x^6))^(-2) = ((2x^6)/(3y^4))^2 = (4x^12)/(9y^8)
The sum of three consecutive odd integers is 201. What is the middle integer?
67