27^5x81^9=(3^3)^5x(3^4)^9=3^15x3^36=3^51

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\(\frac{14^{16}\times21^{32}\times35^{48}}{10^{16}\times35^{32}\times7^{96}}\)

\(=\frac{\left(2\times7\right)^{16}\times\left(3\times7\right)^{32}\times\left(5\times7\right)^{48}}{\left(2\times5\right)^{16}\times\left(5\times7\right)^{32}\times7^{96}}\)

\(=\frac{2^{16}\times7^{16}\times3^{32}\times7^{32}\times5^{48}\times7^{48}}{2^{16}\times5^{16}\times5^{32}\times7^{32}\times7^{96}}=\frac{2^{16}+7^{96}+3^{32}+5^{48}}{2^{16}\times5^{48}\times7^{32}\times7^{96}}\)

\(=\frac{3^{32}}{7^{32}}=\left(\frac{3}{7}\right)^{32}\)

Ta có: 12⁸ . 18¹⁶ = (2².3)⁸ . (3².2)¹⁶ = 2¹⁶ . 3⁸ . 3³² . 2¹⁶ = (2¹⁶ . 2¹⁶).(3⁸.3³²)= 3⁴⁰ . 2³² (đpcm)

Ta có : \(VP=12^8.18^{16}=\left(2^2.3\right)^8.\left(2.3^2\right)^{16}\)

                 \(=2^{16}.3^8.2^{16}.3^{32}\)

                  \(=3^{40}.2^{32}=VT\)

\(\Rightarrowđpcm\)

12⁸.18¹⁶ = (3.2²)⁸.(2.3²)¹⁶ 

              = 3⁸.(2²)⁸.2¹⁶.(3²)¹⁶

              =3⁸.2¹⁶.2¹⁶.3³²

              =(3⁸.3³²).(2¹⁶.2¹⁶)

              =3⁴⁰.2³² (ĐPCM)

Vậy 12⁸.18¹⁶ = 3⁴⁰.2³²

\(16\cdot4^{x+1}=64\)

\(\Leftrightarrow4^{x+1}=4\)

\(\Leftrightarrow x+1=1\)

\(\Leftrightarrow x=0\)

Ta có: 16 x \(4^{x+1}\)=64

Nên \(4^{x+1}\) =64 : 16 = 4=4\(4^1\)

Suy ra x+1 =1 =>x = 0

hc tot nha

\(16.4^{x+1}=64\)

\(\Rightarrow4^{x+1}=64:16\Rightarrow4^{x+1}=4\)

\(\Rightarrow x+1=1\Rightarrow x=0\)

a)\(\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.5\right)^{10}=1^{10}=1\)

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

c)\(\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{2.3}:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{6+2}=\left(\frac{1}{8}\right)^8\)

\(a.\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.\left(5^2\right)^{10}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.25\right)^{10}=5^{10}.\)

\(b.5^2.3^5.\left(\frac{3}{5}\right)^2=\left[5^2.\left(\frac{3}{5}\right)^2\right].3^5=\left(5.\frac{3}{5}\right)^2.3^5=3^2.3^5=3^7\)\(c.\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left[\left(\frac{1}{4}\right)^2\right]^3:\left[\left(\frac{1}{2}\right)^3\right]^2=\left(\frac{1}{4}\right)^6:\left(\frac{1}{2}\right)^6=\left(\frac{1}{4}:\frac{1}{2}\right)^6=\left(\frac{1}{2}\right)^6\)

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