Question 754359
your expression is (3.2 * 10^4) * (4 * 10^-5)


since everything is being multiplied, you can remove the parentheses without affecting the result of the multiplication.


your expression becomes:


3.2 * 10^4 * 4 * 10^-5


you can use the commutative property of multiplication to re-order the terms in the multiplication.


your expression becomes:


3.2 * 4 * 10^4 * 10^-5


you can use the associative property of multiplication to group the terms in the multiplication.


your expression becomes:


(3.2 * 4) * (10^4 * 10^-5)


you can complete the multiplication in the first set of parentheses.


your expression becomes:


12.8 * (10^4 * 10^-5)


you can use the rules of exponent arithmetic to complete the multiplication in the second set of parentheses as follows:


10^4 * 10^-5 = 10^(4 + (-5)) = 10^(4 - 5) = 10^-1


your expression becomes:


12.8 * 10^-1


you need now to convert this to standard scientific notation where there is only digit to the left of the decimal point and the rest of the digits are to the right of the decimal point.


12.8 is equivalent to 1.28 * 10^1


your expression becomes:


1.28 * 10^1 * 10^-1


you can use the associative rule of multiplication to make your expression become:


1.28 * (10^1 * 10^-1)


using the rules of exponent arithmetic, you can simplify the expression within the parentheses as follows:


10^1 * 10^-1 = 10^(1 + (-1)) which becomes 10^(1-1) which becomes 10^0.


your expression becomes:


1.28 * 10^0


this would be your answer in scientific notation.


to confirm, you can convert your original problem from scientific notation to standard notation.


3.2 * 10^4 becomes 32000 in standard notation.
4 * 10^-5 becomes .00004 in standard notation.


(3.2 * 10^4) * (4 * 10^-5) becomes (32000) * (.00004) in standard notation.


perform the multiplication and you get 32000 * .00004 = 1.28


convert this to scientific notation and you get 1.28 * 10^0.