Question

Diego was trying to write (5^2)^4 with a single exponent and wrote (5^2)^4=5^2+^4=5^6. What should the answer be? Explain Diego's error in complete sentences and thoughts.

Answer 1

5^8

Explanation:

Diego added the exponents. This was an error. If he was simplifying

5^2 × 5^4, then he could add the exponents and get a correct answer. But his problem had a power raised to a power. In this case, you multiply the exponents to simplify.

(5^2)^4 means

5^2×5^2×5^2×5^2

which is

5×5×5×5×5×5×5×5

which is 5^8.