Bài 6: 

a: \(2^{27}=8^9\)

\(3^{18}=9^9\)

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)

=10.2>8=20>8

a,\(10^8x2^8=\left(10x2\right)^8=20^8\)

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

Viết các biểu thức sau đây dưới dạng lũy thừa của một số hữu tỉ:

a) \(10^8.2^8=\left(10.2\right)^8=20^8.\)

b) \(10^8:2^8=\left(10:2\right)^8=5^8.\)

c) \(15^8.9^4=15^8.\left(3^2\right)^4=15^8.3^8=\left(15.3\right)^8=45^8.\)

Chúc bạn học tốt!

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

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

a) \(15^8\cdot2^4\)

\(=\left(15^2\right)^4\cdot2^4\)

\(=225^4\cdot2^4\)

\(=\left(225\cdot2\right)^4\)

\(=450^4\)

b) \(27^5:32^3\)

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

\(=3^{15}:2^{15}\)

\(=\left(\dfrac{3}{2}\right)^{15}\)

a)10⁸.2⁸=(10.2)⁸=20⁸

b)10⁸:2⁸=(10:2)⁸=5⁸

c)25⁴.2⁸=(5²)⁴.2⁸=5^2.4.2⁸=5⁸.2⁸=(5.2)⁸=10⁸

a. 10 mũ 8 . 2 mũ 8 = 10 . 2 mũ 8 = 20 mũ 8

b. 10 mũ 8 : 2 mũ 8 = 10 : 2 mũ 8 = 5 mũ 8

c . 25 mũ 4 . 2 mũ 8 = 390625 . 64 = 25000000

Rickroll

a: \(\left(\dfrac{1}{5}\right)\cdot\left(\dfrac{1}{5}\right)^{15}=\left(\dfrac{1}{5}\right)^{1+15}=\left(\dfrac{1}{5}\right)^{16}\)

b: \(\left(-10,2\right)^{10}:\left(-10,2\right)^3=\left(-10,2\right)^{10-3}=\left(-10,2\right)^7\)

c: \(\left[\left(-\dfrac{7}{9}\right)^7\right]^8=\left(-\dfrac{7}{9}\right)^{7\cdot8}=\left(-\dfrac{7}{9}\right)^{56}\)