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# how do i get the answer to 1-(1-.081/12)e-420

i don't know how to simplify the exponent to get the answer

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### 1 Answer

Hi Stacey,

The way you have typed the problem, I am not sure which part is the exponent. I suggest that you use the caret (^) symbol to indicate the exponent. For example, if you mean e to the -420 power, you would put e^-420. Is that what you are going for?

Perhaps you could clarify your question with a comment.

Good luck,

Robert

### Comments

Sorry I put e to say that -420 is the exponent...e really isn't in the equation

Very good Stacey. That makes it much more clear to me. Now this becomes a simple issue of the order of operations. PEMDAS is a good reminder of which operations to do first: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Things inside parentheses are first.

1-(1-.081/12)^-420

Look inside those parentheses. I see a subtraction and a division. PEMDAS tells us to do the division first. (Make sure there isn't a missing set of parentheses from the problem. Sometimes things are presented as fractions with a numerator with many terms. In that case, you have to put all those terms in parentheses or it only looks like a single thing is on the topo of the fraction).

The division is 0.081/12, which is 0.00675, so our problem is now

1-(1-0.00675)^-420

Do the subtraction inside the parentheses.

1-(.99325)^-420

or just

1-.99325^-420

Now, with the things inside the parentheses handled, we have a subtraction and an exponent. Exponents come first. Keep in mind that a negative exponent is just the same as positive exponent but you take the answer and divide one by it.

A^-1 = 1/A

So we have

1-(.99325)^-420

or

1-1/((.99325)^420)

Plugging either into a calculator you get

1 - 17.1949 (rounded off)

-16.1949

This problem can be a bit tricker if you need to keep everything in fractional notation. In that case, remember that .081 is 81/1000, and follow basically the same strategy. Good luck.