8^1/3 / 64^1/3
8^1/3 /64^1/3
8^1/3 = 2
64^1/3 = 4
2/4 = 1/2
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To simplify the expression 8^(1/3) / 64^(1/3), we can start by simplifying the base of each number to a power of 2.
Since 8 = 2^3 and 64 = 2^6, we can rewrite the expression as:
(2^3)^(1/3) / (2^6)^(1/3)
Now, we can apply the power of a power rule which states that (a^m)^n = a^(m*n).
Using this rule, we can simplify further:
2^(3 * 1/3) / 2^(6 * 1/3)
Multiplying the exponents inside the parentheses:
2^1 / 2^2
When we divide powers with the same base, we subtract the exponents.
Therefore, the final answer is:
2^(1-2) = 2^-1 = 1/2
So, 8^(1/3) / 64^(1/3) simplifies to 1/2.