Powers with Negative Exponents A power with a negative exponent is a number that represents the reciprocal of the original exponent. For example: 1/4 =...
A power with a negative exponent is a number that represents the reciprocal of the original exponent. For example:
1/4 = 4-1
1/9 = 9-1
These numbers are also called reciprocal powers. The reciprocal of 1/x is x-1.
Negative exponents are used in various mathematical contexts, such as finding the inverse of a function, calculating antilogarithms, and analyzing geometric properties of shapes.
Here are some important properties of powers with negative exponents:
A-a = 1/aa
(ab)c = ab · c
These properties allow us to manipulate powers with negative exponents in various ways.
Examples:
2-3 = 1/23 = 1/8
(1/3)-4 = (3)4 = 81
0.25-2 = 0.0625
By understanding powers with negative exponents, we gain deeper insights into the mathematical relationships between different numbers and their reciprocal operations