Explanation:
if I understand you correctly, then the problem is
8×(10^-7) × 5×(10^4)
remember, like in additions, in pure multiplications we can permutate (mix) the factors in any way we want.
this is because of the associative property of "+" and "×" operations.
(a×b)×c = a×(b×c)
so, to be sure we know what we are doing, we group the factors based on their type (a power of 10 or not a power of 10) :
8×5 × (10^-7)×(10^4) = 40 × (10^-7)×(10^4)
to calculate the multiplication of the powers of 10 remember, even the base of factors is the same, then we simply add their exponents.
x^a × x^b = x^(a+b)
so, we have
40 × 10^(-7 + 4) = 40 × 10^-3
that is already a valid solution of the multiplication.
now (it was not required in the problem text, but I have to assume it might be in the context), remember the scientific notation :
any number can be represented in the form
a × 10^b
where "a" is a real number with only one digit (not 0) left of the decimal point. and at least one digit (even if it is 0) right of the decimal point.
e.g.
7.0837 × 10⁸
1.500086 × 10^-9
8.0 × 10²
so, what do we have to do to convert
40 × 10^-3
into a true scientific notation ?
well, 40 needs to turn into 4.0. so it has to be divided by 10 (multiplied by 10^-1).
and therefore, to keep the overall value of the number the same, we need to multiply the right side (the power of 10 factor) by 10 (= 10¹).
so,
40×(10^-1) × (10^-3)×(10^1) = 4.0 × 10^-2
that is our true solution.