Final answer:
To find the quotient, express 25 as 5 squared and apply the power of a power rule, resulting in 5 to the power of 12. When dividing by 5 to the power of 7, subtract the exponents to get 5 to the power of 5, which is the correct quotient.
Step-by-step explanation:
To find the quotient in exponential form for the expression 256 ÷ 57, we start by expressing 25 as a power of 5, since 25 is 52. Thus, 256 can be written as (52)6.
Applying the power of a power rule (ab)c = abc, we have (52)6 = 52 × 6 = 512. Now the expression is 512 ÷ 57. according to the laws of exponents for division, to divide two exponential terms with the same base, we subtract the exponents: am ÷ an = am-n. Therefore, 512 ÷ 57 = 512-7 = 55. Hence, the correct quotient in exponential form is 55.