Question

How do zero and negative exponents relate to the problems in the community? Please answer immediately​

Answer 1

Answer:

Specifically, negative exponents are used to represent how small something is. Bats, for example, are pretty tiny creatures. Zoologists use negative exponents to measure different parts of bats, such as their wingspan.

Answer 2

Answer:

Negative exponents and zero exponents often show up when applying formulas or simplifying expressions.

In this section, we will define the Negative Exponent Rule and the Zero Exponent Rule and look at a couple of examples.

Negative Exponent Rule: b^{-2} = \frac{1}{b^n}

In other words, when there is a negative exponent, we need to create a fraction and put the exponential expression in the denominator and make the exponent positive. For example,

3^{-2} = \frac{1}{3^2} = \frac{1}{9}

But working with negative exponents is just rule of exponents that we need to be able to use when working with exponential expressions.

Example:

Simplify: 3-2

Solution:

3-2 = 3{-2} = \frac{1}{3^2} = \frac{1}{9}

Example:

Simplify: \frac{6^{-2}}{7^{-5}}

Solution:

Apply the Negative Exponent Rule to both the numerator and the denominator.

\frac{6^{-2}}{7^{-5}} = 6^{-2} \cdot \frac{1}{7^{-5}} = \frac{1}{6^2} \cdot 7^5 = \frac{7^5}{6^2} = \frac{16,807}{36}

Example:

Simplify: 3-1 + 5-1

Solution:

Apply the Negative Exponent Rule to each term and then add fractions by finding common denominators.

3^{-1} + 5^{-1} = \frac{1}{3} + \frac{1}{5} = \frac{5}{15} + \frac{3}{15} = \frac{8}{15}

Zero Exponent Rule: a0 = 1, a not equal to 0. The expression 00 is indeterminate, or undefined.

In the following example, when we apply the product rule for exponents, we end up with an exponent of zero.

x5x-5 = x5 + (-5) = x0

To help understand the purpose of the zero exponent, we will also rewrite x5x-5 using the negative exponent rule.

x5x-5 = x^5x^{-5} = \frac{x^5}{x^5} = 1

The zero exponent indicates that there are no factors of a number.