Pre-Algebra

4^10 / 4^12

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Write out the division of powers

We are dividing two powers that have the same base (4). This sets us up to use the quotient rule for exponents.
2

Apply the quotient rule for exponents

The quotient rule says: when dividing same bases, subtract the exponents. So we subtract the bottom exponent from the top exponent.
3

Subtract the exponents

10 minus 12 equals -2, so we get 4 to the power of negative 2.
4

Rewrite negative exponent as a fraction

A negative exponent means 'take the reciprocal.' So 4 to the -2 becomes 1 over 4 squared.
5

Evaluate the final fraction

4 squared equals 16, so the final answer is 1 over 16.

Understanding this problem

Learning Insight

When you divide powers with the same base, you subtract exponents because division 'cancels' matching factors. For example, 10 fours on top and 12 fours on bottom means 2 fours are left on the bottom — which is exactly what a negative exponent shows.

Quick Tip

If the top exponent is smaller than the bottom, the answer will always be a fraction less than 1. The result goes on the bottom: .

Common Mistake

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