Simplify - 3 5 3 - 3 5 -2 - - 1 2 2 - -2 - 1 24

(35)^3×(35)^ 2×[(12)^2] ^ 2×124 = (35)^3 2 #160; ×(12)^ 4×124 = 35× 16 ×124 = 485× 24 = 25 (Ans) ...

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Solving a Quadratic Equation by Completion of Squares Method

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Question

Simplify : ${(\frac{3}{5})}^{3} \times {(\frac{3}{5})}^{- 2} \times [(\frac{1}{2})^{2}]^{- 2} \times \frac{1}{24}$

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Solution

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{(\frac{3}{5})}^{3} \times {(\frac{3}{5})}^{3} \times {[{(\frac{1}{2})}^{2}]}^{- 2} \times \frac{1}{24} = \frac{m}{5^{6}}

m

\frac{(3^{3})^{- 2} \times (2^{2})^{- 3}}{(2^{4})^{- 2} \times 3^{- 4} \times 4^{- 2}}

\frac{3^{5} \times 2^{2} \times 7^{- 3}}{7^{- 2} \times 3^{- 3} \times 2^{4}}

{[\frac{2^{2}}{15}]}^{4} \times {[\frac{5^{3}}{2^{3}}]}^{3} + {(\frac{5}{9})}^{3}

\frac{22}{2 \sqrt{3} + 1} + \frac{17}{2 \sqrt{3} - 1}

\frac{78 \sqrt{3} - 5}{m}

m

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