How you do you find the exponent when is divided in scientific notation?

Answer 1

Here are the rules for 'exponents'.

Multiplication ; ADD The expoentns.

e.g. a^(n) x a^(m) = a^(n+m)

Division ; SUBTRACT The expoentns.

e.g.

a^(n) / a^(m) = a^(n -m)

NESTING ; multiplyinng the exponents

(a^(n))^(m)) = a^(nm)

In all cases the coefficient, 'a' in this case MUST be the samer.

e.g.

2^(5) x 2^(3) = 2^(5 + 3) = 2^(8)

2^(5) / 2^(3) = 2^(5-3) = 2^(2)

(2^(5))^(3)) = 2^(5 x 3) = 2^(15)

NB You cannot do 2^(5) x 3^(3) , because the coefficients are different; viz '2' & '3'.

Answer 2

If the exponent of the numerator is a and the exponent of the denominator is b then the crude exponent of their quotient is a-b. However, if the mantissa of the quotient is less than 1 then it needs to be brought into the range [1, 10) and in doing that, the exponent will become a-b-1.