29292391
Description
Mind Map by Joseph Gianotti, updated more than 1 year ago
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Created by Joseph Gianotti
over 3 years ago
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Power and Roots
- First, what does it mean to put a number to a power? Or to give the number an exponent?
- Exponent
- A quantity representing the power to which a given
number or expression is to be raised, usually expressed
as a raised symbol beside the number or expression.
- Okay… cool.
What is that in
english?
- An exponent essentially means a number is multiplied times itself the number of
times inside the exponent.
- Example:
- 4^3=4*4*4=64. Now, it gets more complex
than this when we add in variables and
fractions, but that is in the most basic
terms what an exponent is.
- Next, what is a root, or a radical (they’re basically the same thing)?
- Root
- The root of a number x is another number, which when multiplied by itself a given
number of times, equals x. Usually notated using the symbol
- This means that roots are the opposite of exponents. For
example, a square root of a number aims to find what quantity
times itself would yield the original number.
- Example:
- ^3√64=What number times itself 3 times yields 64? =4--> 4 *4*4 = 64. A radical symbol with no
outside number is assumed to notate the square root.
- Okay… so now the rules and properties. Below will be a table of what needs to be known.
- Note:
- A large majority of problems will ask for all positive exponents. In these cases, you will use the
negative rule to move the terms into the numerator or denominator as appropriate to yield a
positive exponent.
- Take these problems one step at a time
and don’t think too far ahead!
- Take these problems one step at a time
and don’t think too far ahead!
- A large majority of problems will ask for all positive exponents. In these cases, you will use the
negative rule to move the terms into the numerator or denominator as appropriate to yield a
positive exponent.
- Note:
- Okay… so now the rules and properties. Below will be a table of what needs to be known.
- ^3√64=What number times itself 3 times yields 64? =4--> 4 *4*4 = 64. A radical symbol with no
outside number is assumed to notate the square root.
- Example:
- This means that roots are the opposite of exponents. For
example, a square root of a number aims to find what quantity
times itself would yield the original number.
- The root of a number x is another number, which when multiplied by itself a given
number of times, equals x. Usually notated using the symbol
- Root
- Next, what is a root, or a radical (they’re basically the same thing)?
- 4^3=4*4*4=64. Now, it gets more complex
than this when we add in variables and
fractions, but that is in the most basic
terms what an exponent is.
- Example:
- An exponent essentially means a number is multiplied times itself the number of
times inside the exponent.
- Okay… cool.
What is that in
english?
- A quantity representing the power to which a given
number or expression is to be raised, usually expressed
as a raised symbol beside the number or expression.
- Exponent
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