Question

simply:-
81^(-3/4).
explain.

Answer 1

Step-by-step explanation:

81^(-3/4)

cut 4 from 4

3^4*-3/4

27

Answer 2

Answer:

To find: The value of $81^{\frac{-3}{4} }$

Proof:

Prime factorization of 81:

$3|81\\3|27\\3|9\\3|3\\1|1$

= 3 X 3 X 3 X 3

= $3^{4}$

Putting the value of 81 in $81^{\frac{-3}{4} }$, we get:

= $(3^{4})^{\frac{-3}{4} }$

= $(3)^{4 X {\frac{-3}{4} }$                                            [ $(a^{m})^{n} = a^{m X n}$]

= $3^{-3}$

= $\frac{1}{3^{3} }$                                                     [$a^{-m} = \frac{1}{a^{m} }$]

= $\frac{1}{27}$

Hence, $81^{\frac{-3}{4} }$ = $\frac{1}{27}$

Proved.

Hope you got that.

Thank You.