`@` `\text {Ans}`

`\downarrow`

\(3^2\cdot2^5\cdot\left(\dfrac{2}{3}\right)^2\)

`=`\(\left(3\cdot\dfrac{2}{3}\right)^2\cdot2^5\)

`=`\(2^2\cdot2^5=2^7\)

\(3^2\cdot2^5\cdot\left(\dfrac{2}{3}\right)^2\)

\(=2^5\cdot\left(3\cdot\dfrac{2}{3}\right)^2\)

\(=2^5\cdot\left(\dfrac{3\cdot2}{3}\right)^2\)

\(=2^5\cdot2^2\)

\(=2^{2+5}\)

\(=2^5\)

$@$ $\text{Ans}$

$\downarrow$

32⋅25⋅(23)232⋅25⋅(32​)2

$=$(3⋅23)2⋅25(3⋅32​)2⋅25

$=$22⋅25=2722⋅25=27

\(5A=5^2+5^3+5^4+...+5^{100}\)

\(4A=5A-A=5^{100}-5\Rightarrow4A+5=5^{100}-5+5=5^{100}\)

b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)

Viết các biểu thức sau dưới dạng lũy thừa :

5³ . 25² : 5⁴

Trả lời

5³ . ( 5² )² : 5⁴

= 5³ . 5⁴ : 5⁴

= 5⁷ : 5⁴

= 5³

Study well 

\(5^3\cdot25^2\div5^4\)

\(=5^3\cdot\left(5^2\right)^2\div5^4\)

\(=5^3\cdot5^4\div5^4\)

\(=5^{3+4-4}=5^3\)

5³=125

25²=625

5⁴=625

ti ck chéo ko : chuyên toán thcs

a, \(\frac{25.5^3.1}{25.5^2}=\frac{5^2.5^3.1}{5^2.5^2}=\frac{5^5}{5^4}=5\)

b, \(5^2.3^5.\left(\frac{3}{5}\right)^2=5^2.3^5.\frac{9}{25}=5^2.\frac{9}{25}.3^5=9.3^5=3^2.3^5=3^7\)

c, \(\left(\frac{1}{7}\right)^2\cdot\frac{1}{7}\cdot\frac{49}{2}=\frac{1}{49}\cdot\frac{1}{7}\cdot\frac{49}{2}=\frac{1}{49}\cdot\frac{49}{2}\cdot\frac{1}{7}=\frac{1}{2}\cdot\frac{1}{7}=\frac{1}{14}\)

(1+2+3+4+5+....)³

1³ +2³+3³+4³+5³  =(1+2+3+4+5)³

Haiz các bạn kia sai hết oy

1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15²

Bạn có thể kiểm tra lại kết quả của 2 bạn kia ko bao giờ = 225 được

\(\begin{array}{l}a){15^8}{.2^4} = {15^{2.4}}{.2^4} = {({15^2})^4}{.2^4}\\ = {225^4}{.2^4} = {(225.2)^4} = {450^4}\\b){27^5}:{32^3} = {({3^3})^5}:{({2^5})^3}\\ = {3^{3.5}}:{2^{5.3}} = {3^{15}}:{2^{15}} = {\left( {\frac{3}{2}} \right)^{15}}\end{array}\)

a) \(15^8\cdot2^4=3^8\cdot5^8\cdot2^4=9^4\cdot25^4\cdot2^4=\left(9\cdot25\cdot2\right)^4=450^4\) 

b) \(27^5:32^3=\left(3^3\right)^5:\left(2^5\right)^3=3^{15}:2^{15}=\left(\dfrac{3}{2}\right)^{15}\)

c) \(\left(\dfrac{5}{4}\right)^4:\left(\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}:\dfrac{15}{2}\right)^4=\left(\dfrac{1}{6}\right)^4\)

d) \(10^4:16=10^4:2^4=\left(10:2\right)^4=5^4\)

e) \(\left(-2\right)^3.125=\left(-2\right)^3.5^3=\left(-2.5\right)^3=-10^3\)

f) \(64^3:\left(-2\right)^9=64^3:\left(-8\right)^3=\left(64:-8\right)^3=-8^3\)