# 8 Examples to Understand Negative Exponents

##### A quick review of negative numbers

Negative numbers are expressed with a negative sign. For example, -4 is four less than zero.

When you deduct a negative number, you move to the left of the number line, due to the fact that it’s the same as adding a positive number. If you’re adding a negative number you move to the right because it’s the same as deducting a positive number.

Example

```-6 + 2 = -4

6 - (-2) = 8```

When you multiply a negative number by a positive number (or vice versa), the solution will be negative. If you multiply 2 negative numbers or two positive numbers, the outcome will be positive.

Example

```(-6)  (2) = -12

(-6)  (-2) = 12```

Multiplying multiple signs will generally provide you a negative solution, and multiplying the same signs will provide you a positive solution. Always suppose the number is positive if there’s no sign in front of it.

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##### What do negative exponents mean?

There are a few various ways of thinking about negative exponents, but in general, negative exponents are the opposite of positive ones.

All negative exponents can be shown as their positive reciprocal. A reciprocal is a fraction where the numerator and denominator switch places.

Negative exponents can be expressed as the positive reciprocal of the base multiplied by on its own x times.

The larger the negative exponent, the smaller the number it represents. While positive exponents show repeated multiplication, negative exponents represent repeated division. That’s why 2-4is significantly greater than 2-9.

##### Solving of Negative Exponents
###### Multiplication
• If the bases of values are alike then add the exponents. Remember the rules for the addition and subtraction of negative numbers.

Example

4-24-6 = 4-8

• If the bases are not same but the exponents are the same, first of all multiply the bases then leave the exponents as they are.
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Example

4-65-6 = 20-6

• If there’s nothing in common (base or exponent), start solving the equation. Flip exponents into their reciprocals and then multiply.

Example

###### Division
• If the bases are alike then, subtract the exponents.

Remember to convert the exponent and make it positive, if required.

Example

• If the exponents are alike but the bases are different then divide the bases first.

Example

• If there is nothing in common then solve the equations.

Example