# What is the rule for a base with a negative exponent?

## What is the rule for a base with a negative exponent?

Negative numbers with exponents If the base is negative and the exponent is an even number, the final product will always be a positive number. If the base is negative and the exponent is an odd number, the final product will always be a negative number.

What happens when a positive number has a negative exponent?

A positive number with a negative exponent will always give a positive number. For example, 2-3 = 1/8, which is a positive number.

### Can a power with a positive base ever yield a negative value?

Statement is false. Result can be negative or positive it depends from the base and exponent. Very important to remember, if exponent is negative number, that base can’t be zero.

Can you have a negative exponent of 0?

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

#### What does a negative exponent mean?

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

What does a base raised to a negative exponent mean?

The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base. So 2^(-4) = 1/(2^4) = 1/(2*2*2*2) = 1/16. The answer is 1/16. Have a blessed, wonderful New Year!

## Why must negative exponents be changed into positive exponents?

Why can base of exponential function be negative?

Because of their inability to consistently increase or decrease and restrictions on the domain, exponential functions cannot have negative bases.

### How do we interpret positive zero and negative exponents?

When the value of a is smaller than the value of b, we arrive at the rule for a negative exponent. Remember, an expression with a negative power is moved to the oppostite side of the fraction bar as a positive power. Should the values of a and b be the same, we have the rule for a zero exponent.

Why can the base be negative in an exponential function?

#### How do you calculate negative exponents?

The procedure to use the negative exponents calculator is as follows: Enter the base and exponent value in the respective input field Now click the button “Solve” to get the result Finally, the value of the given exponent will be displayed in the output field

What to do when dividing negative exponents?

Divide expressions with negative exponents. To divide expressions with negative exponents, all you have to do is move the base to the other side of the fraction line. So, if you have 3 -4 in the numerator of a fraction, you’ll have to move it to the denominator.

## How do you solve negative exponents?

A trick to solve negative exponent is to make a fraction. Put one on the top and put your base on the bottom. Your base should be to the power of the exponent except make sure to do it without the negative sign. Let’s try this with 2^-3. First, put one on the top and the base on the bottom.

How do you explain negative exponents?

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, “x –2” (pronounced as “ecks to the minus two”) just means “x 2, but underneath, as in “. Write x –4 using only positive exponents.

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