Laws of Exponents Vocabulary
A number that, when multiplied by itself, produces the
given number.
Laws of Exponents
For example, since 16 = 4×4, 4 is the square root of 16. A
square root of a non-negative number can be thought of
as the length of a side of a square whose area equals the
given non-negative number.
Power
The taking of a root of a number.
A number whose cube root is an integer.
Perfect Square
Perfect Cubes
Root/Radical
Square Root
For example, 8 is a perfect cube because its cube root is
the integer 2.
A number whose square root is an integer.
For example, 4 is a perfect square because its square root
is the integer 2.
A short way of writing the same number multiplied by
itself several times, written as an, in which an means a × a
× a . . . n times.
The following is a list of laws useful for combining
exponents of numbers:
Multiplication: axay = ax+y
Division: ax/ay = ax-y
Power of a power: (ax)y = axy
Negative exponent: a-x = 1/ax
Any number, except zero, with the exponent 0 is equal to
1. For example, 1000 = 1.
Cube Root
Exponent
Rational Number
The result obtained when multiplying numbers, vectors,
matrices, etc.
A number that can be written as a fraction, or as finite or
repeating decimals.
The square root of 2 (1.414 213 6...) is not a rational
number.
A fraction as the power.
Product
A number used to indicate the number of times a term is
used as a factor to multiply itself. The exponent is
normally placed as a superscript after the term.
A number or an expression, when multiplied together
three times, produces a given number.
Rational Exponents
For example, the cube root of 8 is 2, since 23 = 8.
Integers
Negative (Inverse) exponent: a-x = 1/ax
Law of Product
Power of a power: (ax)y = axy
Law of Quotient
Low of Power
Division: ax/ay = ax-y
Multiplication: axay = ax+y
Law of Inverse
Any whole number and/or the additive inverse of a whole
number is an integer.
Law of Zero Power
Any number, except zero, with the exponent 0 is equal to
1. For example, 1000 = 1.
Base
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