Question

Which of the following is equal to the expression (8x)^-2/3 (27x)¯1/3
1) 1/12x
2) 3/4x
3) 12×3
4) 3/4x

Answers

  1. The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

    How to evaluate the expression?

    The expression is given as:
    (8x)^-2/3 * (27x)^-1/3
    Evaluate the exponent 8^-2/3
    (8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3
    Evaluate the exponent (27x)^-1/3
    (8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3
    Multiply 1/4 and 1/3
    (8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3
    Evaluate the exponent
    (8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)
    This gives
    (8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)
    So, we have
    (8x)^-2/3 * (27x)^-1/3 = 1/12x
    Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x
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