Question

27. Simplify: 27^(-2/3)÷9^(1/2)×3^(-3/2)​

Answer 1

Hope it will help you....

Answer 2

Concept:

This question requires us to have knowdge on basic arithematic operatins and how to solve roots.

Given:

The following equation is given:

${27^{(-\frac{2}{3}) } } \frac{ 1}\sqrt{9} \times {3^{\frac{-3}{2} } }}$

To find:

We need to find the value of the given equation.

Solution:

Now,

${3^{3} ^{(-\frac{2}{3}) } } \frac{ 1}{3 \times {3^{\frac{-3}{2} } }}$

⇒${3^{-2} } \times } \frac{ 1}{{3^{1-\frac{3}{2} } }}$

⇒${3^{-2} } \times {{3^{\frac{1}{2} } }}$

⇒${3^{-2+\frac{1}{2} } }$

⇒${3^{\frac{-4+1}{2} } }}$

⇒${3^{\frac{-3}{2} } }}$

⇒$\frac{1}{3^{\frac{3}{2} } }$

⇒$\frac{1}{3\sqrt{3} }$

Therefore the value of the given equation is $\frac{1}{3\sqrt{3} }$