Like so many other tools of mathematics, exponents are shortcuts. Multiplication is another example of a mathematical shortcut — multiplying a first number by a second is a shortcut for adding. Write the first number down again and again until you’ve written it down the number of times equaling the second number, and add them all together; that’s the multiplication shortcut. A base number to the power of an exponent is almost the same thing. Write the base number down again and again until you’ve written it down the number of times expressed in the exponent — but this time multiply the numbers together. That’s how you get rid of exponents.

## Expanding

Write each base a number of times equal to the exponent. Multiply the bases together.

For example, 2^5 can be written as 2 * 2 * 2 * 2 * 2, or 32.

Take into account negative exponents. A negative exponent is the same as a positive, except that the base number is written as its inverse before multiplying.

For example, 5^(-3) can be written as (1/5)*(1/5)*(1/5), which equals 1/(5_5_5), or 1/125.

Apply the previous two rules as many times as necessary to expand an expression.

If the expression were 2^4 * 3^3 * 4^-2, it could be rewritten as 2 * 2 * 2 * 2 * 3 * 3 * 3 / 4 * 4. That would simplify to 16 * 27 / 16, or 27.

## Scientific Notation

Move the decimal point the number of places expressed in the power of 10. For example, a number like 3.5 x 10^3 can be written without the power of 10 by moving the decimal point three places to the right. So 3.5 x 10^3 = 3,500.

Watch for negative exponents, and move the decimal point in the opposite direction if the power of 10 is negative. As an example, 5.98 x 10^-4 can be written without the power of 10 by moving the decimal point four places to the left. So 5.98 x 10^-4 = 0.000598.

Simplify the expression before eliminating the exponents. For example, suppose you have (6.626 x 10^-34) x (2 x 10^31). Multiply the both the coefficients first and then the exponential terms. So you would calculate (6.626 x 2) x (10^-34 x 10^31) = 13.252 x 10^-3 = 0.013252.