When powers are the same, bases are different in division?

Yes, when dividing exponents with the same power but different bases, you can apply the power of a quotient property.

Power of a Quotient Property Explained

According to the provided reference, to divide exponents where the powers are the same and the bases are different, we use the Power of a Quotient Property. This property is mathematically represented as:

a^m ÷ b^m = (a ÷ b)^m

This means you can divide the bases a and b first, and then raise the result to the power of m.

Examples and Applications

Here are a few examples to illustrate this property:

• Example 1: 6² ÷ 3²

  Applying the power of a quotient property:

  (6 ÷ 3)² = 2² = 4

• Example 2: 10³ ÷ 2³

  Applying the power of a quotient property:

  (10 ÷ 2)³ = 5³ = 125

Summary

In summary, when you are dividing exponential expressions with different bases but the same exponent, you divide the bases and keep the exponent the same. This simplifies the division process significantly.