Trả lời:

a, \(15^8.9^4\)

\(=15^8.\left(3^2\right)^4\)

\(=15^8.3^8\)

\(=45^8\)

b, \(27^2:25^3\)

\(=\left(3^3\right)^2:\left(5^2\right)^3\)

\(=3^6:5^6\)

\(=\left(\frac{3}{5}\right)^6\)

Hok Tốt!!!!

a. 15⁸ . 9⁴

= 15⁸ . (3²)⁴

= 15⁸.3⁸

= (15.3)⁸

= 45⁸

b. 27² : 25³

= (3³)² : (5²)³

= 3⁶ : 5⁶

= \(\left(\frac{3}{5}\right)^6\)

49 ^ 50 hay 49^500 vậy bạn?

Nếu là 49^ 500 thì 49^500>5^500>3^400

a) \(\left(\frac{1}{16}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2^4}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left[\left(\frac{1}{2}\right)^4\right]^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{4.25}\div\left(\frac{1}{2}\right)^{30}\)

\(=\left(\frac{1}{2}\right)^{100}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{100-30}=\left(\frac{1}{2}\right)^{70}\)

b) \(584^{100}\div292^{100}=\left(584-292\right)^{100}=292^{100}\)

c) \(125^4\cdot16^3=\left(5^3\right)^4\cdot\left(2^4\right)^3=5^{3\cdot4}\cdot2^{4\cdot3}=5^{12}\cdot2^{12}=\left(5+2\right)^{12}=7^{12}\)

ta có :

3² = 9 

3³ = 27 > 25 

3⁴ = 81

3⁴ = 243 < 250

nhưng 3⁶ = 729 > 250

vậy với số mũ n = 3,4,5 ta có : 25 < 3ⁿ < 250

25 < 3ⁿ < 250

\(\Leftrightarrow\)3³ \(\le\) 3ⁿ \(\le\)3⁵

\(\Leftrightarrow\)3 \(\le\)n \(\le\)5

\(\Leftrightarrow\)n = { 3; 4; 5 }

a: \(\frac34+x=\frac34\)

=>\(x=\frac34-\frac34\)

=>x=0

b: \(3^8=6561\)

c: \(\frac{x}{y}=\frac45\)

=>\(\frac{x}{4}=\frac{y}{5}=\frac{4}{x}=\frac{5}{y};\frac{y}{x}=\frac54\)

d: 3x=8y

=>\(\frac{x}{8}=\frac{y}{3};\frac{x}{y}=\frac83;\frac{8}{x}=\frac{3}{y};\frac{y}{x}=\frac38\)

e: Số đối của 7/-5 là \(\frac75\)

0,25 = (0,5)²

\(\dfrac{1}{49}\) = (\(\dfrac{1}{7}\))²

- \(\dfrac{27}{125}\) = (- \(\dfrac{3}{5}\))³

 \(\dfrac{81}{16}\) = ( \(\dfrac{9}{4}\))²

\(\dfrac{169}{196}\) = (\(\dfrac{13}{14}\))²

3².3².3ⁿ=3⁸

n=4

Ko biết đề có phải thế này ko, bạn viết khó hiểu quá ??

\(3^2\cdot\left(3^3\right)^n=3^8\)

\(3^{3n}=3^6\)

=> 3n = 6

=> n = 2

a: $2^6\cdot 3^3={\left(2^2\cdot 3\right)}^3={12}^3$

b: $6^4\cdot 8^3=2^4\cdot 3^4\cdot 2^9=2^{13}\cdot 3^4$

c: $16\cdot 81={36}^2$

d: ${25}^4\cdot 2^8={100}^4$