Question

[watashi wa madoka desu]

Rút Gọn

a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}\)

Answer 1

[Despacito]

a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}=\frac{\left(5^3\right)^{100}.2^{160}}{5^{289}.\left(2^2\right)^{80}}=\frac{5^{300}.2^{160}}{5^{289}.2^{160}}=5^{300-289}=5^{11}\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}=\frac{\left(3^2\right)^8.\left(2^3\right)^8}{3^8.\left(3^3\right)^3.2^{24}}=\frac{3^{16}.2^{24}}{3^8.3^9.2^{24}}=\frac{3^{16}}{3^{17}}=\frac{1}{3}\)

Answer 2

[nguyen thi bao tien]

a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}=\frac{\left(5^3\right)^{100}.2^{160}}{5^{289}.\left(2^2\right)^{80}}=\frac{5^{300}.2^{160}}{5^{289}.2^{160}}=5\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}=\frac{\left(3^2\right)^8.\left(2^3\right)^8}{3^8.\left(3^3\right)^3.2^{24}}=\frac{3^{16}.2^{24}}{3^8.3^9.2^{24}}=\frac{3^{16}.2^{24}}{3^{17}.2^{24}}=\frac{1}{3}\)