Simplify

  1. (a)

    Simplify 5−2(6x−1)5-2(6x-1).

  2. (b)

    Simplify (27b9a6)−1/3\left(\dfrac{27b^9}{a^6}\right)^{-1/3}.

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Worked solution

2(a)

1. Expand the bracket, taking care of the negative multiplier.

5−2(6x−1)=5−12x+25 - 2(6x - 1) = 5 - 12x + 2

2. Collect the constant terms.

5−12x+2=7−12x5 - 12x + 2 = 7 - 12x

Answer

7−12x7 - 12x

2(b)

1. Use the negative index to write the reciprocal with a positive fractional index.

(27b9a6)−1/3=(a627b9)1/3\left(\dfrac{27b^9}{a^6}\right)^{-1/3}=\left(\dfrac{a^6}{27b^9}\right)^{1/3}

2. Apply the cube root to the numerator and denominator.

(a627b9)1/3=(a6)1/3(27b9)1/3=a23b3\left(\dfrac{a^6}{27b^9}\right)^{1/3}=\dfrac{(a^6)^{1/3}}{(27b^9)^{1/3}}=\dfrac{a^2}{3b^3}

Answer

a23b3\dfrac{a^2}{3b^3}

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