Properties of exponents
We will show 8 properties of exponents. Let x and y be a number not equal to zero and let n and m be any integers
Property #1
x
^{0} = 1
Example: 4
^{0} = 1 and (2500000000000000000000)
^{0} = 1
Property #2
x
^{n} × x
^{m} = x
^{n + m}
Example: 4
^{6} × 4
^{5} = 4
^{6 + 5} = 4
^{11}
Property #3
x
^{n} ÷ x
^{m} = x
^{n − m}
Example: 4
^{6} ÷ 4
^{5} = 4
^{6 − 5} = 4
^{1}
Property #4
(x
^{n})
^{m} = x
^{n × m}
(5
^{2})
^{4} = 5
^{2 × 4} = 5
^{8}
Property #5
(x × y)
^{n} = x
^{n} × y
^{n}
(6 × 7)
^{5} = 6
^{5} × 7
^{5}
Property #6
x
^{-n} = 1 ÷(x
^{n}) = 1/(x
^{n})
8
^{-4} = 1 ÷ (8
^{4}) = 1 / (8
^{4})
Property #7
(x/y)
^{n} = x
^{n} / y
^{n}
(8/5)
^{4} = 8
^{4} / 5
^{4}
Property #8
Any questions about properties of exponents? Let me know.
Need a math tutor?
Get an answer in 10 minutes or less from a math expert!
Justanswer features top-notch math experts handpicked by personnel after they have taken and
passed a rigourous math test and after their
credentials have been verified by a third party
Most math experts have bachelor's or master's degree in math or a related field