Question

Simplify : [(64)^-1/6 × (216)^-1/3 × (81)^1/4]/[(512)^-1/3 × (16)^1/4 × (9)^-1/2

Answer 1

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Answer 2

Answer:

$\frac{(64)^{-1/6} \times (216)^{-1/3} \times (81)^{1/4}}{(512)^{-1/3} \times (16)^{1/4} \times (9)^{-1/2}}=3$

Step-by-step explanation:

Given expression can be simplified using rules of indices.

Given the expression

            $\frac{(64)^{-1/6} \times (216)^{-1/3} \times (81)^{1/4}}{(512)^{-1/3} \times (16)^{1/4} \times (9)^{-1/2}}=\frac{(2^{6})^{-1/6} \times (6^{3})^{-1/3} \times (3^{4} )^{1/4}}{(8^{3} )^{-1/3} \times (2^{4} )^{1/4} \times (3^{2} )^{-1/2}}$

Using $({x^{a}})^{b} =x^{ab}$

                                                  $=\frac{2^{-6/6} \times 6^{-3/3} \times 3^{4/4}}{8^{-3/3} \times 2^{4/4} \times 3^{-2/2}}$

                                                  $=\frac{2^{-1} \times 6^{-1} \times 3^{1}}{8^{-1} \times 2^{1} \times 3^{-1}}$

Using $x^{-a} =\frac{1}{x^{a}}$

                                                  $=\frac{8 \times 3\times 3}{2 \times 2\times 6}$

                                                  $=3$

Thus the value of given expression is 3.