6^((1)/(6))*2^((5)/(6))*3^((7)/(6)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) 6root(3)(3) (B) 2^((5)/(36))*3^((7)/(36)) (C) 36^((35)/(216)) (D) root(3)(6^(13))

Question

Bytelearn · Accepted Answer

Combine like terms: Combine the terms with the same base. We notice that 6 can be written as 2 * 3, so we rewrite the expression by combining the terms with the same base. 6^((1)/(6))*2^((5)/(6))*3^((7)/(6)) = (2 * 3)^((1)/(6))*2^((5)/(6))*3^((7)/(6))Apply power property: Apply the power of a product property. Using the property (ab)^n = a^n * b^n, we can rewrite the expression as: (2^1 * 3^1)^((1)/(6))*2^((5)/(6))*3^((7)/(6)) = 2^((1)/(6)) * 3^((1)/(6)) * 2^((5)/(6)) * 3^((7)/(6))Combine terms with same base: Combine the terms with the same base using the property a^m * a^n = a^(m+n). Combine the terms with base 2 and base 3 separately: 2^((1)/(6) + (5)/(6)) * 3^((1)/(6) + (7)/(6))Perform exponent addition: Perform the addition of the exponents. 2^((1)/(6) + (5)/(6)) = 2^((6)/(6)) = 2^1 = 2 3^((1)/(6) + (7)/(6)) = 3^((8)/(6)) = 3^((4)/(3))Simplify the expression: Simplify the expression. The simplified expression is: 2 * 3^((4)/(3))Find equivalent expression: Look for the equivalent expression among the answer choices. The expression 2 * 3^((4)/(3)) does not match any of the answer choices directly. We need to check if we can rewrite it in a different form to match one of the choices.Rewrite using cube root: Rewrite the expression using the cube root. 3^((4)/(3)) can be written as the cube root of 3 raised to the 4th power, which is root(3)(3^4). So the expression becomes: 2 * root(3)(3^4)Check rewritten expression: Check if the rewritten expression matches any of the answer choices. The expression 2 * root(3)(3^4) still does not match any of the answer choices. We need to check if we made a mistake in our calculations or if we need to rewrite the expression further.Correct previous mistake: Realize that there is a mistake in the previous steps. Upon reviewing the steps, we realize that we have not considered the multiplication of 2 with the cube root of 3^4. We need to correct this.

Full solution

More problems from Multiplication with rational exponents

Related topics