Final answer:
To express 6 to the power of negative 1 as a fraction, we write it as 1/6. A negative exponent indicates that the base of the power should be in the denominator of a fraction with a positive exponent.
Step-by-step explanation:
Expressing numbers with negative exponents as fractions is a basic concept in algebra. When we have a number like 6 to the power of negative 1, or 6-1, this is the same as saying '1 divided by 6 to the power of positive 1'. The negative exponent indicates that the base (which is 6 in this instance) should be moved from the numerator to the denominator of a fraction, with the power becoming positive. Thus, 6-1 equates to 1/6.
Looking at other examples, such as 3-4, we can follow the same rule. We convert this to a fraction by placing 3 to the power of 4 in the denominator: 1/34 or 1/81. Here, the negative exponent implies a 'division' rather than a 'multiplication', as it flips the base to the denominator. Therefore, with negative exponents, we create a fraction where the numerator is always 1 (1/xn), and the exponent is positive in the denominator.
To provide further illustration, scientific notation often uses negative exponents to represent small decimal numbers. For example, 2.4 x 10-2 means that we move the decimal point two places to the left to get 0.024. Consequently, the negative exponent is a handy notation for representing small numbers in a compact and understandable form.