Answer:
4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal
Explanation:
Simplify the following:
(2^(1/3))^7
Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.
Multiply exponents. (2^(1/3))^7 = 2^(7/3):
2^(7/3)
Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.
2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):
2^(6/3) 2^(1/3)
Hint: | Divide 6 by 3.
6/3 = (3×2)/3 = 2:
2^2 2^(1/3)
Hint: | Evaluate 2^2.
2^2 = 4:
Answer: 4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal