Question

So sánh hai số: \(a=15^{120}:25^{60}\)  và   \(b=2^{45}.2^{15}.4^{60}\)

Answer 1

\(a=15^{120}:25^{60}\)

\(a=3^{120}.5^{120}:\left(5^2\right)^{60}\)

\(a=3^{120}.5^{120}:5^{120}\)

\(a=3^{120}\)

\(b=2^{45}.2^{15}.4^{60}\)

\(b=2^{60}.\left(2^2\right)^{60}\)

\(b=2^{60}.2^{120}\)

\(b=2^{180}\)

ta co  \(a=3^{120}=\left(3^2\right)^{60}=9^{60}\)

            \(b=2^{180}=\left(2^3\right)^{60}=8^{60}\)

vi \(9^{60}>8^{60}\) nen \(3^{120}>2^{180}\)

         vay  \(a>b\)