Explanation:
To simplify the expression [5(8^(1/3) + 27^(1/3))]^(11/4), first simplify the expressions inside the parentheses:
8^(1/3) is the cube root of 8, which is 2, because 2^3 = 8.
27^(1/3) is the cube root of 27, which is 3, because 3^3 = 27.
Now, substitute these values back into the expression:
[5(2 + 3)]^(11/4)
Now, simplify the addition inside the parentheses:
[5(5)]^(11/4)
Next, simplify the multiplication inside the outer parentheses:
[25]^(11/4)
Now, raise 25 to the power of 11/4:
25^(11/4) = (5^2)^(11/4)
Apply the power rule (a^(m/n) = (a^(m/n))^(n)):
(5^(2*(11/4)))
Now, multiply the exponents:
5^(22/4)
Simplify the exponent by finding a common factor between 22 and 4, which is 2:
5^(11/2)
So, [5(8^(1/3) + 27^(1/3))]^(11/4) simplifies to 5^(11/2).
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Answers & Comments
Explanation:
To simplify the expression [5(8^(1/3) + 27^(1/3))]^(11/4), first simplify the expressions inside the parentheses:
8^(1/3) is the cube root of 8, which is 2, because 2^3 = 8.
27^(1/3) is the cube root of 27, which is 3, because 3^3 = 27.
Now, substitute these values back into the expression:
[5(2 + 3)]^(11/4)
Now, simplify the addition inside the parentheses:
[5(5)]^(11/4)
Next, simplify the multiplication inside the outer parentheses:
[25]^(11/4)
Now, raise 25 to the power of 11/4:
25^(11/4) = (5^2)^(11/4)
Apply the power rule (a^(m/n) = (a^(m/n))^(n)):
(5^(2*(11/4)))
Now, multiply the exponents:
5^(22/4)
Simplify the exponent by finding a common factor between 22 and 4, which is 2:
5^(11/2)
So, [5(8^(1/3) + 27^(1/3))]^(11/4) simplifies to 5^(11/2).