# Negative exponents and scientific notation

• oscar_brown
In summary, the first problem can be solved by multiplying (10^2)^8 by 10^-6, giving a result of 10^22. The second problem can be solved by dividing 1.2x10^-6 by 4.2x10^-2, resulting in a quotient of 2/7 multiplied by 10^-4, which is approximately equal to 2.9x10^-5.
oscar_brown
holy cow i feel dumb...

i know these are super easy but i just can't figure it out.

1. --- (10^2)^8 divided by (10^-2)^3

2. --- 1.2x10^-6 divided by 4.2x10^-2

if anyone can give me a kick in the brain it would be awsome

1.--- 10^22?
2. -- 2.9x10^5??

Last edited:
The first one is correct. The second is not (but only by a sign, typo ?). To check, multiply your quotient by the divisor to see if you get the dividend.

$$(10^2)^8\div(10^{-2})^3=10^{16}\div10^{-6}=10^{16}\cdot10^6=10^{22}$$

$$1.2\cdot10^{-6}\div\left(4.2\cdot10^{-2}\right)= 1.2\cdot10^{-6}\cdot\frac{1}{4.2}\cdot10^2= \frac{1.2}{4.2}\cdot10^{-4}=\frac27\cdot10^{-4}\approx2.9\cdot10^{-5}$$

no it wasn't a typo...just dumb
thank you so much, it is amazing how fast you forget stupid things

## 1. What is a negative exponent?

A negative exponent represents the reciprocal of a number raised to a positive exponent. For example, 10-2 is the same as 1/102 which is equal to 0.01.

## 2. How do you simplify expressions with negative exponents?

To simplify expressions with negative exponents, you can move the base and exponent to the opposite location in the fraction. For example, 2-3 can be rewritten as 1/23 which is equal to 1/8.

## 3. What is scientific notation?

Scientific notation is a way to write numbers that are very large or very small in a shorter and more concise form. It is written in the form a x 10n, where a is a number between 1 and 10 and n is an integer.

## 4. How do you convert a number into scientific notation?

To convert a number into scientific notation, you need to move the decimal point to the left or right until there is only one non-zero digit to the left of the decimal point. Count the number of times you moved the decimal point and use that number as the exponent. For example, 0.0000000012 can be written as 1.2 x 10-9.

## 5. How can you perform calculations with numbers in scientific notation?

To perform calculations with numbers in scientific notation, you can use the rules of exponents. When multiplying, add the exponents and when dividing, subtract the exponents. For example, (2 x 103) x (5 x 102) is equal to 10 x 105 which can be simplified to 1 x 106 or 106.

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