=(2²⁰¹⁴.3²⁰¹⁴/3²⁰¹⁵.2²⁰¹²) -1 = 2²/3  -1 = 1/3

tính giá trị biểu thức nha 

\(\frac{4^{1007}.9^{1007}}{3^{2015}.16^{503}}=\frac{4^{1007}.\left(3^2\right)^{1007}}{3^{2015}.\left(4^2\right)^{503}}=\frac{4^{1007}.3^{2014}}{3^{2015}.4^{1006}}=\frac{4}{3}\)

\(\frac{4^{1007}.9^{1007}}{3^{2015}.2^{2016}}=\frac{\left(2^2\right)^{1007}.\left(3^2\right)^{1007}}{3^{2015}.2^{2016}}\)

\(=\frac{2^{2014}.3^{2014}}{3^{2015}.2^{2016}}=\frac{2^{2014}.3^{2014}}{3^{2014}.2^{2014}.3.2^2}\)

\(=\frac{1}{3.2^2}=\frac{1}{3.4}=\frac{1}{12}\)

Rút gọn

\(\frac{4^{1007}\cdot9^{1007}}{3^{2015}\cdot2^{2016}}=\frac{\left(2^2\right)^{2007}\cdot\left(3^2\right)^{1007}}{3^{2015}\cdot2^{2016}}\)

\(=\frac{2^{2\cdot1007}\cdot3^{2\cdot1007}}{3^{2015}\cdot2^{2016}}=\frac{2^{2014}\cdot3^{2014}}{3^{2015}\cdot2^{2016}}\)

\(=\frac{1}{3.2^2}=\frac{1}{12}\)

Vậy ...

hok tót .

\(\frac{4^{1007}.9^{1007}}{3^{2015}.2^{2016}}=\frac{\left(2^2\right)^{1007}.\left(3^2\right)^{1007}}{3^{2015}.2^{2016}}=\frac{2^{2014}.3^{2014}}{3^{2015}.2^{2016}}=\frac{1}{\left(3^{2015}:3^{2014}\right).\left(2^{2016}:2^{2014}\right)}=\frac{1}{3.2^2}=\frac{1}{3.4}=\frac{1}{12}\)

Lưu ý: Phải tách ra mỗi lũy thừa sao cho hợp với tử số(mẫu số)

Chúc bạn học tốt!

\(\frac{4^{1007}.9^{1007}}{3^{2015}.16^{503}}=\frac{4^{1007}.\left(3^2\right)^{1007}}{3^{2015}.\left(4^2\right)^{503}}=\frac{4^{1007}.3^{2014}}{3^{2015}.4^{1006}}=\frac{4}{3}\)

\(\frac{4^{1007}.9^{1007}}{3^{2015}.16^{503}}=\frac{4^{1007}.\left(3^2\right)^{1007}}{3^{2015}.\left(4^2\right)^{503}}=\frac{4^{1007}.3^{2014}}{3^{2015}.4^{1006}}=\frac{4}{3}\)

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