Powers with the same base can be divided by subtracting their exponents.

Quotient of powers examples. The quotient of powers rule is used to simplify the problem of division that involves exponents. Rewrite powers of products and quotients. The quotient of powers property states when dividing powers with the same base, the exponents are subtracted, assuming the base is not equal to {eq}0 {/eq}.

About 7.26 km2 example 3 simplifying an expression simplify a10 — a6 ⋅ a7 — a4. (5/7) 2 = 5 2 /7 2 = 25 /49. Learn how this rule works along with examples in simple and complex division.

In this tutorial, you'll see how to use the quotient of powers rule to simplify an expression. • no quotients are raised to powers. When you multiply two powers with the same base, you add the exponents.

For example, (3⁵⋅x³)² can be written as 3¹⁰⋅x⁶. Don’t worry if that doesn’t make sense off the bat; • no powers are raised to powers.

Examples of how to find the quotient of powers of rational and equal bases division of rational and equal base powers. Below are two examples of the quotient of powers theorem in effect: According to the property, the common exponent on the division of numbers can be equally distributed among the numerator and denominator.

In this process, we subtract. Rewrite powers of products and quotients. The quotient of powers rule states that when dividing two powers with the same base, just subtract the exponents.