Question

Quotient rule of exponents practice

Answer 1

The quotient rule of exponents states that when dividing two exponential expressions with the same base, you subtract the exponents.

For example, if we have the expression (x^3)/(x^2), we can apply the quotient rule of exponents by subtracting the exponents of x:

x^3 / x^2 = x^(3-2) = x^1 = x

Let's practice using the quotient rule of exponents with some more examples:

1) (a^5)/(a^3)
To divide the expression, we subtract the exponents:
(a^5)/(a^3) = a^(5-3) = a^2

2) (z^8)/(z^4)
Again, subtract the exponents to divide:
(z^8)/(z^4) = z^(8-4) = z^4

3) (2^6)/(2^3)
Apply the quotient rule by subtracting the exponents:
(2^6)/(2^3) = 2^(6-3) = 2^3 = 8

4) (m^2)/(m^4)
When the exponent in the denominator is greater than the exponent in the numerator, the result will be a fraction with a negative exponent:
(m^2)/(m^4) = 1/(m^(4-2)) = 1/m^2

5) (10^5)/(10^5)
Since the exponents are the same, the result will be 1:
(10^5)/(10^5) = 1

These are some examples of how to use the quotient rule of exponents in practice. Remember to subtract the exponents when dividing exponential expressions with the same base.