Question

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal:

Answer 1

Consider the expression $(8.1\cdot 10^{-4})^2.$

Use main properties for powers:

1. $(a\cdot b)^m=a^m\cdot b^m;$

2. $(a^m)^n=a^{m\cdot n};$

3. $a^m\cdot a^n=a^{m+n}.$

Then

$(8.1\cdot 10^{-4})^2=8.1^2\cdot (10^{-4})^2=65.61\cdot 10^{-4\cdot 2}=65.61\cdot 10^{-8}=6,561\cdot 10^{-2}\cdot 10^{-8}=6,561\cdot 10^{-10}.$

The result in scientific notation is $6,561\cdot 10^{-10}.$

The result as a decimal is $0.0000006561.$