Question

Simplify 81 with an exponent of -3/4 and explain please! Thank you!!

Answer 1

- so you need to know that when we have exponent fractional so than the numerator sign the exponent of this term and the denominator sign the indice of radical so than in this case there is 81 on exponent (-3) inside radical indice 4

- like one example if there is (x) on exponent (-1/2) so this sign that there is squaroot (1/x)
so (1/x) because there is x on exponent (-1)

- so in presently case (exersice) we have

Answer 2

\[\sqrt[4]{(1/81)^{3}}\]

Answer 3

- so but 81 equal 3 on exponent 4

Answer 4

- so than inside root will be 3 on exponent 4 and this all on exponent (-3) and from this result 3 on exponent (-12) inside root indice 4

Answer 5

\[\sqrt[4]{(3)^{(-12)}}=3^{(-12/4)}=3^{(-3)}=1/3^{3}=1/27\]