Question

[nguyen ba manh]

tính 

(1/2)¹⁰  -(1/4)²⁰ 

Answer 1

[Trần Thanh Phương]

\(\left(\frac{1}{2}\right)^{10}-\left(\frac{1}{4}\right)^{20}\)

\(=\left(\frac{1}{2}\right)^{10}-\left[\left(\frac{1}{2}\right)^2\right]^{20}\)

\(=\left(\frac{1}{2}\right)^{10}-\left(\frac{1}{2}\right)^{40}\)

\(=\left(\frac{1}{2}\right)^{10}-\left(\frac{1}{2}\right)^{10}\cdot\left(\frac{1}{2}\right)^{30}\)

\(=\left(\frac{1}{2}\right)^{10}\cdot\left[1-\left(\frac{1}{2}\right)^{30}\right]\)

\(=\frac{1}{2^{10}}\cdot\frac{1-2^{30}}{2^{30}}\)

\(=\frac{1-2^{30}}{2^{40}}\)