Final answer:
The expression 1/5 * 1/5 * 1/5 using exponents is written as (1/5)^3. When evaluated, it equals 1/125 because you multiply the numerators to get 1 and the denominators to get 125.
Step-by-step explanation:
Writing and Evaluating an Exponential Expression
To write the expression 1/5 * 1/5 * 1/5 using exponents, we recognize that we are multiplying the same base (1/5) repeatedly. In exponential terms, this is expressed as raising the base to the power of the number of times it is being multiplied. Therefore, 1/5 multiplied by itself three times is written as (1/5)3.
Evaluating this exponential expression simply means calculating its value. Since exponents indicate repeated multiplication, (1/5)3 equals 1/5 * 1/5 * 1/5. When you multiply the fractions, you multiply the numerators (top numbers) and the denominators (bottom numbers) separately. Therefore, 1*1*1 equals 1 for the numerator, and 5*5*5 equals 125 for the denominator, resulting in the fraction 1/125.
The final value of the expression (1/5)3 is 1/125.