# How do you multiply a negative exponent?

## How do you multiply a negative exponent?

To multiply by a negative exponent, subtract that exponent. To divide by a negative exponent, add that exponent.

What happens when an exponent is negative?

What is negative exponent? A negative exponent helps to show that a base is on the denominator side of the fraction line. In other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.

### How do you solve a negative exponent?

A negative exponent is defined as the multiplicative inverse of the base, raised to the power which is opposite to the given power. In simple words, we write the reciprocal of the number and then solve it like positive exponents. For example, (2/3)-2 can be written as (3/2)2.

What does 10 to the minus 3 mean?

Here we have an expression involving power of ten with a negative exponent. The base is 10 and the exponent is −3. Step 2: In normal course the value of 10-3 can be found by multiplying the base 10 three times in the denominator and putting a 1 in the numerator. 10-3 = = 0.001.

#### What is 10 to the power of minus 9 called?

Negative powers

Name Power SI prefix
millionth −6 micro
billionth −9 nano
trillionth −12 pico

Which is an example of multiplying negative exponents?

Multiplying negative exponents. For exponents with the same base, we can add the exponents: a -n ⋅ a -m = a -(n+m ) = 1 / a n+m. Example: 2 -3 ⋅ 2 -4 = 2 -(3+4) = 2 -7 = 1 / 2 7 = 1 / (2⋅2⋅2⋅2⋅2⋅2⋅2) = 1 / 128 = 0.0078125. When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:

## Can a negative exponent be transformed into a reciprocal fraction?

Similarly, with a negative exponent, it can either be left as it is, or transformed into a reciprocal fraction. For example: 2 − 2 ⋅ 2 − 3 = 2 − 2 – 3 = 2 − 5 = ( 1 2) 5.

Are there any rules for dividing exponents in multiplication?

As for multiplication, there are two basic rules for dividing exponents. The first rule – when bases are the same, their exponents are subtracted. For example: 2 2: 2 = 2 2 2 = 2 2 – 1 = 2 1 = 2, which can easily be checked since 4: 2 = 2. For example: 2 − 2: 2 − 1 = 2 − 2 2 − 1 = 2 − 2 − (− 1) = 2 − 1 = 1 2.

### How to multiply exponents when the bases are the same?

Multiplying exponents with different bases. When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first: a n ⋅ b n = (a ⋅ b) n. Example: 32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144. When the bases and the exponents are different we have to calculate each exponent and then multiply: