Question

Which is the simplified form of the expression (6^-4)^-9/6^6

Answer 1

Should be 6^30

Explanation:

Answer 2

Given expression:
`(((6^(-4))^(-9)))/(6^6)`.

First we would apply exponents of exponent rule on the top.

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

Therefore,

`((6^(-4))^(-9)) = (6)^(-4* -9) = (6)^(36)`

=
`(((6^(-4))^(-9)))/(6^6) = (6^36)/(6^6)`

Applying quotient rule of exponents.

`(a^m)/(a^n) = a^(m-n)`

`Therefore \ (6^(36))/(6^6) =6^(36-6)`

=
`6^(30)`

Therefore,
`6^(30)` is the simplified form of the expression
`(((6^(-4))^(-9)))/(6^6).`