\(7^2.49^3.7^7=7^2.\left(7^2\right)^3.7^7=7^2.7^6.7^7=7^{15}\)

\(3^5.9^4.27^2.81=3^5.\left(3^2\right)^4.\left(3^3\right)^2.3^4=3^5.3^8.3^6.3^4=3^{23}\)

a) \(7^2.49^3.7^7=7^2.7^6.7^7=7^{15}\)

b) \(3^5.9^4.27^2.81=3^5.3^8.3^6.3^4=3^{23}\)

\(7^2.49^3.7^7\)

= \(7^7.\left(7^2\right)^3.7^7\)

= \(7^7.7^6.7^7\)

= \(7^{7+6+7}\)
= \(7^{20}\)

\(3^5.9^4.27^2.81\)

= \(3^5.\left(3^2\right)^4.27^2.81\)

= \(3^2.3^8.\left(3^6\right)^2.3^3\)

= \(3^2.3^8.3^{12}.3^3\)

= \(3^{2+8+12+3}\)

= \(3^{25}\)

3.9³.27²

=3.(3²)³.(3³)²

=3¹.3^2.3+3^3.2

=3¹+3⁶+3⁶

=3¹⁺⁶⁺⁶

=3¹³

kq là3¹³

3.9³.27²

=3.(3²)³.(3³)²

=3¹.3^2.3+3^3.2

=3¹+3⁶+3⁶

=3¹⁺⁶⁺⁶

=3¹³

Bài 6: 

a: \(2^{27}=8^9\)

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

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)

a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)

b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)

c: \(16\cdot81=36^2\)

d: \(25^4\cdot2^8=100^4\)

`@` `\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

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

\(=5^2\cdot\dfrac{5}{3}\cdot\dfrac{3}{5}\cdot\dfrac{3}{5}=5^2\cdot\dfrac{3}{5}=5\cdot3=15^1\)

    3 \(\times\)2⁵\(\times\) (\(\dfrac{2}{3}\))²

= \(\dfrac{2^5.2^2.3}{3^2}\)

= \(\dfrac{2^7}{3}\)

Lời giải:

\(3.2^5.(\frac{2}{3})^2=\frac{3.2^5.2^2}{3^2}=\frac{2^7}{3}=(\frac{2}{\sqrt[7]{a}})^7\).