Question

Find the value (1/27)⅔​

Answer 1

Answer:

the value of the expression is 1/9

Step-by-step explanation:

Given  :

we are given a expression

$(\frac{1}{27})^\frac{2}{3}$

To Find :

The value of the given expression

Solution :

Since the given expression is

$(\frac{1}{27})^\frac{2}{3}$

here we can observe that ($3^3=27$)

So here replace 27 by $3^3$

by replacing we get

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

simplifying the above expression we get

$(\frac{1}{3^3})^\frac{2}{3}=(3^{-3})^\frac{2}{3}=3^{-3\ \text{x}\ \frac{2}{3}$

$3^{-3\ \text{x}\ \frac{2}{3} }= 3^{-2}=\frac{1}{9}$

Hence we have calculated that the value of the expression is 1/9

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Answer 2

The value  of $(\frac{1}{27} )^{\frac{2}{3} }$ is  $\frac{1}{9}$.​

Step-by-step explanation:

Given:

The expression is $(\frac{1}{27} )^{\frac{2}{3} }$ .

To Find:

The value  of $(\frac{1}{27} )^{\frac{2}{3} }$ .

Concept Used:

The exponent rule  $(a^{m} )^{n} =a^{mn}$.

Where $(a^{m} )^{n} =a^{mn}$  is the power rule for exponents  Multiply the exponent by the power to raise a number with an exponent to that power.

Solution:

As given,the expression is $(\frac{1}{27} )^{\frac{2}{3} }$ .

Simplify the expression.

$(\frac{1}{27} )^{\frac{2}{3} }$$(\frac{1}{27} )^{\frac{2}{3} }=(\frac{1}{3^{3} } )^{\frac{2}{3} }$

                  $=({3^{-3} } )^{\frac{2}{3} }$

   Applying $(a^{m} )^{n} =a^{mn}$

                   $=3^{-2}$

                  $=\frac{1}{3^{2} }$

                  $=\frac{1}{9}$

Thus,the value  of $(\frac{1}{27} )^{\frac{2}{3} }$ is  $\frac{1}{9}$.​

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