Question

simplify: 9^1/3*27^-1/2/3^1/6*3^-2/3

Answer 1

I am able to understand your question but if it is


9 raise to the power( 1 upon 3) * 27 raise to the power (-1 upon 2) /3 raise to the power (1 upon 6 )*3 raise to power. (- 2 upon 3)
Answer

Answer 2

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