Question

(1/6^-2×9^-3/2 (1/27)^-4/3×8^-2/3​

Answer 1

Answer:

\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}=3^{\frac{-1}{3}}361×3−32931×27−21=33−1

Step-by-step explanation:

Given Expression: \frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}361×3−32931×27−21

We have to simplify it,

Consider,

\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}361×3−32931×27−21

\implies\frac{(3^2)^{\frac{1}{3}}\times(3^3)^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹361×3−32(32)31×(33)−21

Now we use law of exponent, (x^a)^b=x^{a\times b}(xa)b=xa×b

\implies\frac{3^{2\times{\frac{1}{3}}}\times3^{3\times{-\frac{1}{2}}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹361×3−3232×31×33×−21

\implies\frac{3^{\frac{2}{3}}\times3^{\frac{-3}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹361×3−32332×32−3

We use another law of exponent, x^a\times x^b=x^{a+b}xa×xb=xa+b

\implies\frac{3^{\frac{2}{3}+\frac{-3}{2}}}{3^{\frac{1}{6}+(-\frac{2}{3})}}⟹361+(−32)332+2−3

\implies\frac{3^{\frac{-5}{6}}}{3^{\frac{-1}{2}}}⟹32−136−5

We use another law of exponent, \frac{x^a}{x^b}=x^{a-b}xbxa=xa−b

\implies3^{\frac{-5}{6}-\frac{-1}{2}}⟹3