Question

How to solve this sum showing steps​

Answer 1

Given: An expression $(27)^{-\frac{2}{3} }$

To find: The solution of this expression

Solution:

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

• Express with a positive exponent using $a^{-n} = \frac{1}{a^{n} }$

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

• Write the number in exponential form with the base of $3$.

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

• Simplify the expression by multiplying the exponents and hence, by reducing $3$.

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

• Evaluate the power and do the square of $3$.

$\frac{1}{9}$

Final Answer:

Hence, the value of the expression $(27)^{-\frac{2}{3} }$ , is $\frac{1}{9}$ .