Scientific Notation problem?

Question

4.0 x 10^2 x 1/10^3 x (6.5 x 10^-2)/1 =

When adding the 10^2 with the 10^-2 is comes out as 10^0. I'm not sure how to solve the rest of the problem...?

Also, in a problem such as this.... 6 x (1.5 x 10^-2)^2 would you add the exponents (outside of the parenthesis) or multiply them? If you add them, it also comes out to 10^0, so this one confused me as well.

Answer 1

When multiplying numbers with exponents, add the exponents.

When dividing numbers with exponents, subtract the denominator exponent from the numerator exponent.

Examples:

10^2 x 10^3 = 10^(3+2) = 10^5

10^4 / 10^-2 = 10^(4 -(-2)) = 10^6

10^3 x 10^-3 = 10^0 = 1

(10^4)3 = 10^4 x 10^4 x 10^4 = 10^12 (multiple the exponent inside the parenthesis by the exponent outside the parenthesis)

Answer 2

4.0 x 10^2 x 1/10^3 x (6.5 x 10^-2)/1

=4.0 x 6.5 x 10^2 /10^3 x 10^-2

= 28 x 10^(2 - 3 - 2)

= 2.8 x 10 x 10^(-3)

= 2.8 x 10^(-2)

6 x (1.5 x 10^-2)^2

= 6 x 1.5^2 x 10^(-4)

Just remember

A^a x A^b = A(a+b)

(A^a)^b = A^(ab)