Pre-Algebra

9^16 / 9^17

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Write the division as one expression

We have a fraction with the same base (9) on top and bottom. This sets us up to use the exponent division rule.
2

Apply the quotient rule for exponents

When you divide two powers with the same base, subtract the exponents. Keep the base the same.
3

Subtract the exponents

16 minus 17 equals -1, so we get 9 to the power of negative 1.
4

Convert negative exponent to a fraction

A negative exponent means take the reciprocal. So is the same as .

Understanding this problem

Learning Insight

The quotient rule works because division cancels matching factors. means 16 nines multiplied together, and means 17 nines. All 16 nines on top cancel with 16 of the 17 nines on the bottom, leaving one 9 in the denominator — which is exactly .

Quick Tip

If the bigger exponent is on the bottom, your answer will be a fraction less than 1. If it's on top, the answer will be greater than 1. Use this to quickly check if your answer makes sense.

Common Mistake

Students often divide the exponents instead of subtracting them, writing instead of . Always SUBTRACT exponents when dividing same-base powers.