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# Unit 2 Exponents

Exponents Exponents tell us how many we multiply a number by itself. In the example 5^3 (5x5x5), 5 is the base and 3 is called the exponent.
Product Rule When like bases are being multiplied, their exponents can be added together. (X^a * X^b = X^a+b)
Quotient Rule When like bases are being divided, their exponents can be subtracted. (X^a / X^b = X^a-b)
Power Rule When an exponent is raised to another exponent, the exponents can be multiplied. ((X^a )^b = X^ab)
Negative Exponents Rule When an exponent is a negative number, we can think of it as taking the reciprocal. (X^-a = 1/X^a)
Squaring A Negative Number in Parentheses The number will always be positive. Example (-3)^2 = 9
Squaring a Negative Number without Parentheses The number will always be negative. Example -3^2 = -9
Squares and Square Roots Solutions Squaring a number is the inverse of taking the square root. Talking the square root of a number technically results in two solutions. For example square root of 16 = 4 and -4, because 4^2 = 16 and (-4)^2 = 16.
Cubes and Cube Roots Solutions Cubing a number, or raising a number to a power of 3, is the inverse of taking the cube root. For example, the cube root of 8 = 2, because 2*2*2=8. Also, a cube root of a negative number will always be negative. Think about this…
Scientific Notation This is the shorthand way of writing really large or really small numbers. NX10^a where N<10 and a = integers.
Standard Form This is the really large or really small numbers before they are converted to scientific notation and vice versa.
LARS Used when adding, subtracting, multiplying and dividing with scientific notation. Left Add Right Subtract
Rules For Converting Standard To Scientific 1. Create a number between 1 and 10. 2. Count the number times that you moved the decimal (Exponent#). Left to Right Negative and Right to Left Positive.
Rules For Converting Scientific to Standard 1. Move the decimal the same number of places as the exponent. 2. If the exponent is positive, move the decimal to the right. 3. If the exponent is negative, move the decimal to the left. (add zeros as needed)
Zero Exponent Rule Anything raised to the zero exponent will equal 1. Example - 2^0=1
One Exponent Rule Anything raised to the first power/exponent will equal its self. Example - 5^1 = 5
Negative Perfect Cubes These will always be negative. Example (-5)^3 = (-5)*(-5)*(-5) = -125 and -5^3 = -5*5*5 = -125
Created by: hmcarew