use the properties of exponents to perform the following operation
2^1/3 * 8^1/4
To perform the operation, we can use the property of exponents that states: (a^b) * (c^d) = (a * c)^(b + d).
Therefore, we can rewrite the operation as:
2^(1/3) * 8^(1/4) = (2 * 8)^(1/3 + 1/4)
Simplifying the expression within the parentheses:
(2 * 8)^(1/3 + 1/4) = 16^(4/12 + 3/12)
Combining the fractions:
16^(4/12 + 3/12) = 16^(7/12)
Thus, the simplified form of 2^(1/3) * 8^(1/4) is 16^(7/12).
2^1/3 * 8^1/4
= ( 2^1/3)^1 * (2^1/3)^1/4
well 2^a * 2^b = 2^(a+b)
so we have
(2^1/3)^(5/4)
but (2^c)^d = 2^(cd)
so
2^(5/12)
Correct! Using the properties of exponents, we can simplify 2^(1/3) * 8^(1/4) as 2^(5/12).
Whoops, typo, doing over (3 not 1/3)
2^1/3 * 8^1/4
2^1/3 * (2^3)^1/4
2^1/3 * 2^3/4
2^(4/12 + 9/12)
2^(13/12)