Question

Simplify 27 to the negative 2 thirds power.

Answer 1

Answer:

1/9

Step-by-step explanation:

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

To simplify the expression with fractional exponent , we write the base 27 in exponential form

$27= 3 \cdot 3 \cdot 3= 3^3$

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

Now we apply exponential property

$(a^m)^n= a^{mn}$

$3^{3 \cdot {-\frac{2}{3}}$

$3^{-2}$

Write the answer with positive exponent, move the exponent to the denominator.

$\frac{1}{3^2} =\frac{1}{9}$

Answer 2

27^(-2/3)=1/((∛27)^2)

=1/3^2

=1/9