a) \(3^6.3^7\) \(=3^{13}\)

b) \(x^{10}:x^6:x\)

\(=x^{10}:x^7\)\(=x^3\)

c) \(a^5.a^9=a^{14}\)

\(a,=3^{6+7}=3^{13}\\ b,=x^{10-6-1}=x^3\\ c,=a^{5+9}=a^{14}\\ d,=2^3\cdot2^{15}\cdot2^{16}=2^{34}\\ e,=5^6\cdot5^5\cdot5^5=5^{16}\\ f,=a^{10+4-12}=a^2\)

d) \(2^3.8^5.16^4\)

\(=2^3.\left(2^3\right)^5.\left(2^4\right)^4\)

\(=2^3.2^{15}.2^{16}\)

\(=2^{34}\)

e) \(25^3.5^5.3125\)

\(=\left(5^2\right)^3.5^5.5^5\)

\(=5^6.5^5.5^5\)

\(=5^{16}\)

f) \(a^{10}.a^4:a^{12}\)

\(=a^{14}:a^{12}\)

\(=a^2\)

a) \(k=\frac{2^{11}.9^2}{3^5.16^2}=\frac{2^{11}.\left(3^2\right)^2}{3^5.\left(2^4\right)^2}=\frac{2^{11}.3^4}{3^5.2^8}=\frac{8.1}{3.1}=\frac{8}{3}\)

b)  \(N=\frac{9^3.27^2}{6^2.3^{10}}=\frac{\left(3^2\right)^3.\left(3^3\right)^2}{\left(2.3\right)^2.3^{10}}=\frac{3^6.3^6}{2^2.3^2.3^{10}}=\frac{3^{12}}{4.3^{12}}=\frac{1}{4}\)

c)\(P=\frac{\left(3^3\right)^{25}.5^3.\left(2^3\right)^4}{\left(5^2\right)^2.\left(3^4\right)^{11}.2^{11}}=\frac{3^{75}.5^3.2^{12}}{5^4.3^{44}.2^{11}}=\frac{3^{31}.1.2}{5.1.1}=\frac{3^{31}.2}{5}=....\)

a) \(K=\frac{2^{11}\cdot9^2}{3^5\cdot16^2}=\frac{2^{11}\cdot3^4}{3^5\cdot2^8}=\frac{2^3}{3}=\frac{8}{3}\)

b) \(N=\frac{9^3\cdot27^2}{6^2\cdot3^{10}}=\frac{3^6\cdot3^6}{2^2\cdot3^2\cdot3^{10}}=\frac{1}{4}\)

c) \(P=\frac{27^{15}\cdot5^3\cdot8^4}{25^2\cdot81^{11}\cdot2^{11}}=\frac{3^{45}\cdot5^3\cdot2^{12}}{5^4\cdot3^{44}\cdot2^{11}}=\frac{3\cdot2}{5}=\frac{6}{5}\)

a, \(\dfrac{3^8}{3^4}+2^2.2^3\)
= 3⁴ + 2⁵
= 113
b, 3.4² - 2.3²
= 3.(4² - 2.3)
= 3.(16 - 6)
= 3.10
= 30
c, \(\dfrac{4^6.3^4.9^5}{6^{12}}\)

= \(\dfrac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{\left(2.3\right)^{12}}\)

= \(\dfrac{2^{12}.3^4.3^{10}}{2^{12}.3^{12}}\)

= \(\dfrac{3^{14}}{3^{12}}\)

= 3²
@Dương Tuyết Mai

(6^3.8^4):12^3

=> ( 216 . 4096 ) : 1728

=> 884736 : 1728 = 512

\(\left(6^3\times8^4\right)\div12^3\)

\(=\left(216\times4096\right)\div1728\)

\(=884736\div1728\)

\(=512\)

(6³×8⁴)÷12³

=(216×4096)÷1728

=884736÷1728

=512