a) \(10^n+1-6\cdot10^n=\left(1-6\right)10^n+1=-5\cdot10^n+1\)

b)  \(90\cdot10^n-10^2-2+10^n+1=\left(90-1+1\right)\cdot10^n-2+1=90\cdot10^n-1\)

c)  \(2,5\cdot56^n-3=\frac{5}{2}\cdot56^n-3\)

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\(d,2,5.5^{n-3}.2.5+5^n-6.5^{n-1}=5.5.5^{n-3}+5^n-6.5^{n-1}=5^2.5^{n-3}+5^n-6.5^{n-1}\)

  \(=5^{n-3+2}+5^n-6.5^{n-1}=5^{n-1}\left(1+5-6\right)=5^{n-1}.0=0\)

a, \(10^{n+1}-6.10^n=10^n\left(10-6\right)=4.10^n\)

b. \(2^{n+3}+2^{n+2}-2^{n+1}+2^n=2^n\left(2^3+2^2-2+1\right)=2^n\left(8+4-2+1\right)=11.2^n\)

Mình cho bạn tự làm câu d  mà không làm thôi làm cho vậy

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

= \(10^n (10-6)=4.10^n\)

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

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

= \(2^n (8+4-2+1)\)

\(= 11.2^n\)

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

\(= 10^k(90-2+1)\)

= \(89.10^k\)

\(D/ 2,5 . 5^{n-3} . 10+5^n -6 .5^{n-1}\)

\(= 5.5.5^{n-3} +5^n-6.5^{n-1}\)

= \(5^2 .5^{n-3}+5^n-6.5^{n-1} \)

= \(5^{n-3+2}+5^n -6.5^{n-1}\)

\(= 5^{n-1}(1+5-6)\)

= \(5^{n-1}.0\)

= 0

a) 10^{n + 1} - 6.10ⁿ

= 10ⁿ . 10 - 6 . 10ⁿ

= 10ⁿ . (10 - 6)

= 10ⁿ . 4

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

= 2ⁿ . 2³ + 2ⁿ . 2² - 2ⁿ . 2 + 2ⁿ . 1

= 2ⁿ . (8 + 4 - 2 + 1)

= 2ⁿ . 11

a: \(10^{n+1}=10^n\cdot10\)

b: \(2^{n+3}+2^{n+1}-2^{n+1}+2^n\)

\(=2^n\cdot8+2^n=9\cdot2^n\)

c: \(90\cdot10^k-10^{k+2}+10^{k+1}\)

\(=90\cdot10^k+10^k\cdot10-10^k\cdot100=0\)

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:

\(2,5\times5^{n-3}\times10+5^n-6\times5^{n-1}=2,5\times\dfrac{5^n}{5^3}\times10+5^n-6\times\dfrac{5^n}{5}\) \(=2,5\times\dfrac{5^n}{125}\times10+5^n-\dfrac{6}{5}\times5^n\) \(=0,2\times5^n+5^n-1,2\times5^n\) \(=5^n\times\left(0,2+1-1,2\right)=5^n\times0=0\)

1a) \(10^{n+1}-6\cdot10^n\)

\(=10^n\cdot10-6\cdot10^n\)

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

\(=10^n\cdot4\)

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

\(=2^n\cdot2^3+2^n\cdot2^2-2^n\cdot2+2^n\)

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

\(=2^n\cdot11\)

c) \(90\cdot10^k-10^{k+2}+10^{k+1}\)

\(=90\cdot10^k-10^k\cdot10^2+10^k\cdot10\)

\(=10^k\left(90-10^2+10\right)=0\)

d) \(2,5\cdot5^{n-3}\cdot10+5^n-6\cdot5^{n-1}\)

\(=\dfrac{2,5\cdot10\cdot5^n}{5^3}+5^n-\dfrac{6\cdot5^n}{5}\)

\(=\dfrac{5^n}{5}+5^n-\dfrac{6\cdot5^n}{5}\)

\(=\dfrac{5^n+5^n\cdot5-6\cdot5^n}{5}=\dfrac{5^n\left(5-6\right)+5^n}{5}=0\)

2. \(M+\left(6x^2-4xy\right)=7x^2-8xy+y^2\)

\(M=\left(7x^2-8xy+y^2\right)-\left(6x^2-4xy\right)\)

\(M=7x^2-8xy+y^2-6x^2+4xy\)

\(M=7x^2-6x^2-8xy+4xy+y^2\)

\(M=x^2-4xy+y^2\)

1a) 10^{n + 1} - 6.10ⁿ = 10ⁿ.10 - 6.10ⁿ = 10ⁿ.(10 - 6) = 10ⁿ.4

b) 2^{n + 3} + 2^{n + 2} - 2^{n + 1} + 2ⁿ = 2ⁿ.8 + 2ⁿ.4 - 2ⁿ.2 + 2ⁿ = 2ⁿ.(8 + 4 - 2 + 1) = 2ⁿ.11

c) 90.10^k - 10^{k + 2} + 10^{k + 1} = 90.10^k - 10^k.100 + 10^k.10 = (90 - 100 + 10).10^k = 20.10^k

d) 2,5.5^{n - 3}.10 + 5ⁿ - 6.5^{n - 1} = 2,5.5ⁿ : 125.10 + 5ⁿ - 6.5ⁿ: 5 = 0,2.5ⁿ + 5ⁿ - 1,2.5ⁿ = (0,2 + 1 - 1,2).5ⁿ = 0