Final answer:
The equivalent equation to a^5=21 is most closely approximated by a=7, option 4, as 7^5 exceeds 21. There seems to be a typo in the options since none match exactly.
Step-by-step explanation:
The student has asked which equation is equivalent to a^5 = 21. To find the value of 'a', we need to find the fifth root of 21. None of the provided options (a = 4, a = 5, a = 6, a = 7) perfectly satisfy the equation when raised to the power of 5. However, the closest whole number to the fifth root of 21 would be 2, considering 2^5 = 32 which is the closest fifth power that exceeds 21. Since this option is not in the list, we need to recognize that we are dealing with an approximation or a potential typo in the options. The closest option that exceeds 21 when raised to the fifth power is option 4: a = 7, as 7^5 = 16,807.
Given the information provided and based on typical middle school mathematics curriculum which involves solving for roots and exponents, the most likely correct answer among the options presented would be option 4, meaning a = 7.