\(\dfrac{2^3.3^4}{2^3.3^2.5}=\dfrac{1.3^2}{1.1.5}=\dfrac{9}{5}\)

Ta có :2^3.3^4/2^2.3^2.5=2.3^2/1.1.5=2.9/5=\(\dfrac{18}{5}\)

1062882

\(\frac{2^3.3}{2^2.3^2.5}=\frac{2}{3.5}=\frac{2}{15}\)

\(2^3.\frac{3}{2^2}.3^2.5=8.\frac{3}{4}.9.5=6.9.5=54.5=270\)

\(\dfrac{7}{1^3\cdot2^3}+\dfrac{19}{2^3\cdot3^3}+\dfrac{37}{3^3\cdot4^3}+...+\dfrac{29701}{99^3\cdot100^3}\\ =\dfrac{2^3-1^3}{1^3\cdot2^3}+\dfrac{3^3-2^3}{2^3\cdot3^3}+\dfrac{4^3-3^3}{3^3\cdot4^3}+...+\dfrac{100^3-99^3}{99^3\cdot100^3}\\ =\dfrac{2^3}{1^3\cdot2^3}-\dfrac{1^3}{1^3\cdot2^3}+\dfrac{3^3}{2^3\cdot3^3}-\dfrac{2^3}{2^3\cdot3^3}+...+\dfrac{100^3}{99^3\cdot100^3}-\dfrac{99^3}{99^3\cdot100^3}\\ =\dfrac{1}{1^3}-\dfrac{1}{2^3}+\dfrac{1}{2^3}-\dfrac{1}{3^3}+...+\dfrac{1}{99^3}-\dfrac{1}{100^3}\\ =1-\dfrac{1}{100^3}< 1\)

Vậy ...

muốn rút gọn phân số đó ta làm như sau:

\(\frac{2^3\cdot3}{2^2\cdot3^2\cdot5}\)=\(\frac{2}{3\cdot5}\)=\(\frac{2}{15}\)

3⁴:3³=3¹=3

3³.3⁴=3⁷

5².5⁵=5⁷

19¹⁴:19⁷=19⁷

3⁴: 3²= 3^{4- 2}= 3²= 9.

3³. 3⁴= 3^{3+ 4}= 3⁷= 2187.

5². 5⁵= 5^{2+ 5}= 5⁷= 78125.

19¹⁴: 19⁷= 19^{14- 7}= 19⁷= 893871739.

+) \(3^4:3^2=3^{4-2}=3^2\)

+) \(3^3\times3^4=3^{3+4}=3^7\)

+) \(5^2\times5^5=5^{2+5}=5^7\)

+) \(19^{14}:19^7=19^{14-7}=19^7\)

_Chúc bạn học tốt_

Ta có:

\(\frac{2^3.3^4}{2^2.3^2.5}=\frac{2.3^2}{5}=\frac{18}{5}\)

\(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}=\frac{2.11}{5.7}=\frac{22}{35}\)

Ta có:

\(\frac{2^2.2.3^2.3^2}{2^2.3^2.5}\) =\(\frac{2.3^2}{5}\) =\(\frac{18}{5}\)

Vậy

Ta cã: \(\frac{2^3.3^4}{2^2.3^2.5}\)

\(=\frac{2^2.2.3^2.3^2}{2^2.3^2.5}\)

\(=\frac{2.3^2}{5}\)

\(=\frac{18}{5}\)