How do you simplify #9times10^ -31 * (3times10 ^7)^2 #?

1 Answer
Lotusbluete
Nov 9, 2015

#81 * 10^(-17)#

Explanation:

First of all, simplify the square in the second part:

# 9 * 10 ^(-31) * (3 * 10^7)^2 = 9 * 10^(-31) * 3^2 * (10^7)^2#

According to the power rule # (a^n)^m = a^(n*m)#, you can simplify further:

#... = 9 * 10^(-31) * 9 * 10^14#

Now, compute #9 * 9#:

# ... = 81 * 10^(-31) * 10^14#

Use the power rule: #a^n * a^m = a^(n+m)#

# ... = 81 * 10^(-31 + 14) = 81 * 10^(-17)#

This might already be a final answer.

If you would like to formulate the result in the scientific notation, you would need to shift one digit of the #81# and thus increase the exponent of the basis #10# by #1#:

#... = 8.1 * 10^(-16)#.

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