Question

Simplify 27 to the negative 2 thirds power.

Answer 1

27^(-2/3)=1/((∛27)^2)

=1/3^2

=1/9

Answer 2

1/9

Explanation:

`27^{-(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)^{-(2)/(3)}`

Now we apply exponential property

`(a^m)^n= a^(mn)`

`3^{3 \cdot {-(2)/(3)}`

`3^(-2)`

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

`(1)/(3^2) =(1)/(9)`