Maths-
General
Easy

Question

open parentheses square root of x cubed end root close parentheses to the power of a, where x greater or equal than 0 In the given expression, a is a constant. The expression is equivalent to x6, where x ≥ 0. What is the value of a ?

The correct answer is: 4


    Say, a to the power of b equals a to the power of d plus 4 end exponent, then b = d + 4. We use this property to solve the problem.
    Explanations:
    Step 1 of 2:
    We have the given expression open parentheses square root of x cubed end root close parentheses to the power of a, where x ≥ 0.
    Then, open parentheses square root of x cubed end root close parentheses to the power of a equals open square brackets open parentheses x cubed close parentheses to the power of 1 half end exponent close square brackets to the power of a equals open parentheses x to the power of 3 over 2 end exponent close parentheses to the power of a equals x to the power of fraction numerator 3 a over denominator 2 end fraction end exponent
    Step 2 of 2:
    Now, it is said that open parentheses square root of x cubed end root close parentheses to the power of a equals x to the power of 6
    not stretchy rightwards double arrow x to the power of fraction numerator 3 a over denominator 2 end fraction end exponent equals x to the power of 6
    not stretchy rightwards double arrow fraction numerator 3 a over denominator 2 end fraction equals 6
    not stretchy rightwards double arrow a equals 6 cross times 2 over 3 equals 4
    Final Answer:
    The value of a is 4.

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