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Solve the expression$(27)^ {- (2 \div 3)} \div (9)^{ 1 \div 2}$
Given:
$(27)^ {- (2 \div 3)} \div (9)^{ 1 \div 2}$
To do: Solve the given expression
Solution:
We know $27 = 3^3$ and $9 = 3^2$
So it will be $(3^3)^{- \frac{2}{ 3}} \div (3^2)^{\frac{1}{2}}$
using $(p^m)^n = p^{mn}$
$3^-2 \div 3$
$\frac{1}{3^2} \div 3$
$\frac{1}{3^2\times\frac{1}{3}}$
$\frac{1}{3^{-3}}$
Therefore, the value of the expression is $3^{3}$
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