How do you solve a math problem with a negative exponent?

Answer 1

Positive exponents:

y squared, which is written as "y with a small raised 2", means "y to the power 2" , and that is y multiplied by y (Notice that we have used the y twice.)

5 to the power 3 is written as "5 with a small raised 3", and it means "five times five times five" which is 125. (Notice that we have used the 5 three times.

Similarly 10 to the power 6 is written as "10 with a small raised 6", which means "10 x 10 x 10 x 10 x 10 x 10" and is 1,000,000. (Notice that the number 10 has been used 6 times.

When we write the above examples, the 2 and the 3 and the 6 are positive numbers (but we don't use the positive sign.) They are positive exponents.

Negative exponents:

10 to the power negative 2 which is written as "the number 10 with a small raised negative 2" means "the reciprocal of 10 to the power 2", which is "the reciprocal of 10 squared". Now the reciprocal of a number is 1 divided by that number, so the reciprocal of 10 is one over ten which is one tenth, and the reciprocal of 10

squared is 1 divided by 10 squared, which is 1 over 100, one hundredth.

Similarly y to the power minus 4 would be 1 divided by y times y times y times y.

And 6 to the power minus 3 would be 1 over 6 x 6 x 6; that's 1 divided by 216.

Of course if you have a decent hand-held calculator you will find the way to solve a mathematical problem containing exponents from the instruction booklet.. You can also tackle such problems with the "scientific" calculator to be found on most computers. Use the word "calculator" in "search".

That brings up a simple calculator. Then click on "View" followed by "scientific" and you then have a very powerful calculator which will deal with lots of scientific calculations. (Saves brainpower!)