Which of the following is equivalent to ?

To solve this problem, all we need to do is move the decimal point.

Because we have a negative exponent (-3), we have to move our decimal point to the left.

Because our exponent is 3, we will move the decimal point 3 to the left:

Making our answer:

When multiplying exponents, we just add the exponents while keeping the base the same.

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring . We get .

Express as a power of ; that is: .

Then .

Using the properties of exponents, .

Therefore, , so .

When we multiply two polynomials with exponents, we add their exponents together. Therefore,

When adding exponents, you want to factor out to make solving the question easier.

We can factor out to get

.

Now we can add exponents and therefore our answer is

.

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is .

The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is .