Question

Rút gọn các biểu thức:

a) \(^{10^{n+1}}\) -6.\(^{10^n}\)

b) \(^{2^{n+3}}\) +\(^{2^{n+2}}\) - \(2^{n+1}\)+\(^{2^n}\)

c) 90.\(^{10^k}\)-\(^{10^{k+2}}\)+\(10^{k+1}\)

d)2,5.\(^{5^{n-3}}\).10+\(^{5^n}\)-\(^{6.5^{n-1}}\)

Answer 1

a) \(10^{n+1}-6.10^n\)

\(=10^n.10-6.19^n\)

\(=10^n.\left(10-6\right)\)

\(=10^n.4\)

b) \(2^{n+3}+2^{n+2}-2^{n+1}+2^n\)

\(=2^n.2^3+2^n.2^2-2^n.2+2^n.1\)

\(=2^n.\left(2^3+2^2-2+1\right)\)

\(=2^n.11\)

c) \(90.10^k-10^{k+2}+10^{k+1}\)

\(=90.10^k-10^k.10^2+10^k.10\)

\(=10^k.\left(90-10^2+10\right)\)

\(=0\)

d) \(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)

\(=\dfrac{2,5.5^n.10}{5^3}+5^n-\dfrac{6.5^n}{5}\)

\(=\dfrac{5^n}{5}+5^n-\dfrac{6.5^n}{5}\)

\(=\dfrac{5^n+5^{n+1}-6.5^n}{5}=\dfrac{5^n+5^n.5-6.5^n}{5}=\dfrac{5^n\left(1+5-6\right)}{5}=\dfrac{0}{5}=0\)