We van divide the exponents if and only if the bases are the same or the powers are the same. Otherwise, we will need to simplify each exponent and then find the quotient.
1. Same bases:
2^5 / 2^8
We notice that the bases are equal, then the quotient is the same base raised to the difference between powers.
==> 2^5/ 2^8 = 2^(5-8) = 2^-3 = 1/2^3
2. Same powers.
3^5 / 10^5
We notice that the powers are equal
==> 3^5/ 10^5 = (3/10)^5 = (0.3)^5
3. Different bases and powers:
2^3 / 5^2
In this case we need to simplify:
2^3 = 8
5^2 = 25
==> 2^3 / 5^2 = 8/25 = 0.32
We can divide exponential expressions if and only if they have the same base.
Let's see an example:
We'll have to divide a^5 by a^3. Since the exponential expressions have the same base, namely a, we'll just subtract the exponents:
a^5/a^3 = a^(5 - 3) = a^2
Also, if the expressions have coefficients, we can also divide them, only if they have the same base.
The steps to follow are:
- we'll check if the exponentials have the same base;
- we'll divide the coefficients;
- we'll subtract the superscripts;
- we'll put the coefficients first, the base second and the superscripts third.