Multiplying and dividing in scientific notation

I can seem to get the right answer...help?

9x10^ -31 * (3x10 ^7)^2
---------------------------------
2

(first value times the square of the second value all divded by 2)

Start with BEDMAS, brackets, exponents, division, multiplication, addition, subtraction. In the problem that you have you need to raise the single item, therefore no work to be done to the second exponent. In scientific notation you add exponents to multiply, subtract exponents to divide, multiply to raise to an exponent and divide to obtain a radical. You can treat the exponentiation component separately from the other item.

To start, raise the bracket item to the second power so that you have 9 X 10^14. You have squared the 3 and also squared the 10^7. Next step is to multiply this by 9 X 10^-31 which will result in 81 X 10 -16. This divided by 2, or 2 X 10^1, will result in 40.5 X 10^-16. Is there a possibility that you have copied the answer incorrectly? There is also the chance that the answer from the back of the text is wrong.

You probably understood all that so if a text is involved, hope that it is wrong. It has happened in the past.

The answer in the back of the book is right, to within truncation error. St N has made a couple of minor errors in his/her exponents.

9•10^-31 • (3•10^7)² / 2
= 9•10^-31 • 9•10^14 / 2
= (81/2)•10^-17
= 40.5•10^-17
= 4.05•10^1 • 10^-17
= 4.05•10^(1 - 17)
= 4.05•10^-16

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The 1st error is, when you multiply 9•10^14 by 9•10^-31, it is
81•10^-17 (not 10^-16)
The next is that 2 = 2•10^0 (not 10^1)
Then combining those 2 wrong results would give
81•10^-16 / 2•10^1 = 40.5•10^-17 (not 10^-16)
which is 4.05•10^-16, which is the right answer, obtained by canceling errors.

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[9 x 10^ -31 * (3 x 10 ^7)^2 ] / 2 =

[9 x 10^ -31 * 9 x 10^14 ] / 2

(9 * 9 * 10^-31 * 10^14) / 2 =

( 81 * 10^(-31+14) ) / 2 =

(81/2) * 10^-17 =

40.5 * 10^-17 =

4.05 * 10 * 10^-17 =

4.05 * 10^-16

9x10^ -31 * (3x10 ^7)^2
---------------------------------
2
= 9x10^-31 * 9x10^14
--------------------------------
2
= 81x10^-17
----------------
2
= 40.5x10^-17
= 4.05x10^-16
~ 4x10^-16.

(9 x 10^(−31)) x (3 x 10^7)² / 2

= (9 x 10^(−31)) x (9 x 10^14) / 2

= (9 x 9 x 10^(−31+14)) / 2

= (81 x 10^(−17)) / 2

= 40.5 x 10^(−17)

= 4.05 x 10^(−16)

4.0500000000000000*10^-16