Dividing Exponentials

A: Division of Monomials

Remark: To divide exponentials use fourth law of exponents.

Note when dividing exponential expressions with the same base we subtract the exponent on the denominator from the exponent on the numerator.

Note that when you divide by you get 1 since a nonzero constant divided by itself is equal to 1.

Definition: If x is not equal to zero and n is a positive integer

Remark: In certain other problems involving both multiplication and division we need the following law of exponents.

Note when raising a quotient to a power we raise the numerator to the power and divide by the denominator raised to the power.

In performing any calculations follow the order of operations. Here we do the exponentiation before we multiply.

Step 1: Use law V to square the quotient.
Step 2: Use Law III to square the product.
Step 3: Use Law II to square the exponentials.
Step 4: Reduce before you multiply. To reduce we divide numerator and denominator by . Of course when we divide we use law IV.
Step5. Use law I to multiply.