Question

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Answer 1

a: \(C=\dfrac{15^3+5\cdot15^2-5^3}{18^3+6\cdot18^2-6^3}\)

\(=\dfrac{3^3\cdot5^3+5^3\cdot3^2-5^3}{\left(2\cdot3^2\right)^3+6\cdot\left(2\cdot3^2\right)^2-2^3\cdot3^3}\)

\(=\dfrac{5^3\left(3^3+3^2-1\right)}{2^3\cdot3^6+2^3\cdot3^5-2^3\cdot3^3}\)

\(=\dfrac{5^3\left(3^3+3^2-1\right)}{2^3\cdot3^3\left(3^3+3^2-1\right)}=\dfrac{5^3}{2^3\cdot3^3}=\dfrac{125}{216}\)

b: \(D=\dfrac{\left(7^4-7^3\right)^3}{49^3}=\dfrac{\left[7^3\left(7-1\right)\right]^3}{7^6}\)

\(=\dfrac{7^9\cdot6^3}{7^6}=7^3\cdot6^3=42^3=74088\)