Final answer:
The correct expression equivalent to 8 * 8 * 8 * 8 * 8 is A) 8⁵. This is because exponentiation compactly represents repeated multiplication of the same number. Other options provided involve either different operations or incorrect numbers and hence are not equivalent.
Step-by-step explanation:
The student is asked to determine which expressions are equivalent to 8 * 8 * 8 * 8 * 8. This expression can be rewritten using exponents, which is a way of showing repeated multiplication of the same number. The equivalent expression using exponents is 8 to the power of 5, or 8⁵ because the number 8 is multiplied by itself five times. Therefore, the correct option is A) 8⁵.
Option B) 8 * 5 is not equivalent, as it represents the multiplication of 8 and 5, resulting in 40, which is not the same as multiplying 8 by itself five times. Option C) 5⁸ represents the number 5 multiplied by itself 8 times, which is also not equivalent. Option D) 8 + 8 + 8 + 8 + 8 is the addition of the number 8 five times, which results in 40, and again, does not represent the original expression's meaning of repeated multiplication of 8.
Understanding exponentiation is crucial in mathematics as it provides a compact way to represent repeated multiplication and can greatly simplify calculations and expressions. For example, cubing of exponentials means to cube the digit term in the usual way and multiply the exponent of the exponential term by 3, simplifying the overall expression.