how do you solve 27^-4/3 in simpilest form?

Answer 1

Write the number as [ [27^(1/3)] ^4 ] ^-1
Since exponents multiply, this is equivalent to 27^(-4/3)

Take the cube root of 27 ---> 3

Raise it to the 4th power ----> 81 = (3)(3)(3)(3)

Invert it due to the negative exponent (-4/3)

27^(-43) = 1/81

Answer 2

cube root of 27 first
3^ -4
the negative exponent means reciprocal so that is
1/ 3^4 which is 1/81

another method would be to write the prime factorization of 27 as exponents
3^3
then the problem looks like (3^3)^ (-4/3)
when raising a power to a power multiply exponents
3 ^ (3 x -4/3) which gives 3 ^ -4
negative exponents means recriprocal so that would be 1/3^4
which is 1/81

maybe a different way to look at it

Answer 3

this equates to the cube root of 1/27^4
or 3^-4 which is 1/3^4

1/81

Hope this helps! :)

Answer 4

27 is 3 cubed, therefore 27^-4/3 becomes 3^3(-4/3) which is the same as 3^-4=1/81......HOPE THAT HELPS!!!

Answer 5

27 = 3^3

so (3^3)^ -4/3 = 3 ^ ( -4*3/3) = 3^-4 = 1/81