The power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately, before the division is.

Power of a quotient property examples. In this process, we subtract. Pay attention to the last example where we demonstrate the difference between subtracting. In order to use this formula, the bases must be the same.

Simplify ( a 6) 2. Rewrite powers of products and quotients. For example, (3⁵⋅x³)² can be written as 3¹⁰⋅x⁶.

The properties of the log are used to compress numerous logarithms into a single logarithm or to expand a single logarithm into multiple logarithms. So when you divide two powers with the same base, you subtract the exponents. Watch the following video for more examples of how to simplify quotients that contain exponents.

When you have a number or variable raised to a. Suppose you're dividing two expressions with the same exponent, but different bases. 2 4 and 5 4 are two exponential terms in which the exponents are same but their bases are different.

For example, 3 + 4 = 7 (whole number ). In the video lesson, we learned that the quotient of powers with the same base can be simplified by subtracting the exponents,. According to the property, the common exponent on the division of numbers can be equally distributed among the numerator and denominator.

Remember parentheses come before exponents. In the second instance, in order. Numerical example 37 32 = 37 −2= 35.