Question

simplify 9 ^ 1 by 3 into 27 ^ - 1 by 2 by 3 ^ 1 by 6 into 3 ^ - 2 by 3​

Answer 1

Answer:

Answer:

\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}=3^{\frac{-1}{3}}

Step-by-step explanation:

Given Expression: \frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}

We have to simplify it,

Consider,

\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}

\implies\frac{(3^2)^{\frac{1}{3}}\times(3^3)^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}

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

\implies\frac{3^{2\times{\frac{1}{3}}}\times3^{3\times{-\frac{1}{2}}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}

\implies\frac{3^{\frac{2}{3}}\times3^{\frac{-3}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}

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

\implies\frac{3^{\frac{2}{3}+\frac{-3}{2}}}{3^{\frac{1}{6}+(-\frac{2}{3})}}

\implies\frac{3^{\frac{-5}{6}}}{3^{\frac{-1}{2}}}

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

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

\implies3^{\frac{-1}{3}}

Therefore, \frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}=3^{\frac{-1}{3}}