Final answer:
Mathematically, something to the power of negative 1/2 is written as x^-1/2 and equals 1/√x, the inverse square root of x. Negative exponents signify the base number in the denominator indicating a division instead of multiplication, and are used regularly in scientific notation to denote small numbers.
Step-by-step explanation:
Expressing 'something to the power of negative 1/2' can be done mathematically by raising that 'something' to the power of -1/2, which is written as x-1/2. This expression represents the inverse square root of the base number. To understand the negative exponent, consider the rule that a negative exponent indicates that the base is in the denominator. For example, x-n is equivalent to 1/xn. Therefore, x-1/2 equals 1/√x, where √x is the square root of x. The concept of negative exponents is essential in algebra and is often used in scientific notation, where powers of 10 with negative exponents denote very small decimal numbers.
In scientific notation, negative exponents simplify the representation of small numbers. For instance, 0.00045 can be expressed as 4.5 x 10-5. The rules for negative exponents also apply here, where subtracting exponents when dividing (106 divided by 103 equals 103) is analogous to adding in regular arithmetic while considering the sign.
When dealing with powers and their inverses, it's helpful to understand their relationships, such as division being the inverse of multiplication. In the context of negative exponents, this translates to the fact that a negative exponent creates a fraction where the base number becomes the denominator. Similarly, familiar operations like subtraction and division reflect the concept of performing an inverse operation compared to addition and multiplication.