a) Ta có:
\(90.10^k-10^{k+2}+10^{k+1}\)
\(=90.10^k-10^k.10^2+10^k.10\)
\(=10^k\left(90-10^2+10\right)\)
\(=10^k.0=0\)
b) Ta có:
\(2,5.5^{n-3}.10+5^n-6.5^{n-1}\)
\(=2,5.10.5^{n-3}+5^n-6.5^{n-1}\)
\(=5.5.5^{n-3}+5^n-6.5^{n-1}\)
\(=5^2.5^{n-3}+5^n-6.5^{n-1}\)
\(=5^{n-3+2}+5^n-6.5^{n-1}\)
\(=5^{n-1}\left(1+5-6\right)\)
\(=5^{n-1}.0=0\)
a) Rút gọn biểu thức:
\(90\times10^k-10^{k+2}+10^{k+1}=90\times10^k-10^k\times10^2+10^k\times10\) \(=10^k\times\left(90-10^2+10\right)\) \(=10^k\times\left(90-100+10\right)\) \(=10^k\times0=0\)
b) Rút gọn biểu thức:
\(2,5\times5^{n-3}\times10+5^n-6\times5^{n-1}=2,5\times\dfrac{5^n}{5^3}\times10+5^n-6\times\dfrac{5^n}{5}\) \(=2,5\times\dfrac{5^n}{125}\times10+5^n-\dfrac{6}{5}\times5^n\) \(=0,2\times5^n+5^n-1,2\times5^n\) \(=5^n\times\left(0,2+1-1,2\right)=5^n\times0=0\)