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Question

Find the value of 

\[\left( \frac{1}{2} \right)^{-4} + \left( \frac{1}{4} \right)^{-4} + \left( \frac{1}{7} \right)^{-4}.\]

The correct answer is

2673

The values of the individual terms are:
(1/2)-4 = 16,
(1/4)-4 = 256,
(1/7)-4 = 2401.
Adding these together: 16 + 256 + 2401 = 2673. Hence, the correct value is 2.2673.

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Important Questions from Simplification

  1. Simplify the following expression.

    \(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)

  2. The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\)  is:

  3. The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\)  is:

  4. The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\)  is:

  5. The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:

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