Question

How to simplify `(16^(-1/4))^3` using the different laws of exponents?

Answer 1

`1/8`

Explanation:

`"using the "color(blue)"laws of exponents"`

`•color(white)(x)(a^m)^n=a^(mn)`

`•color(white)(x)a^(-m)=1/a^m`

`•color(white)(x)a^(m/n)=(root(n)(a))^m`

`rArr(16^(-1/4))^3=16^(-3/4)`

`color(white)(xxxxxxxx)=1/16^(3/4)`

`color(white)(xxxxxxxx)=1/(root(4)(16))^3=1/2^3=1/8`

Answer 2

`1/8`

Explanation:

Here we will use the following laws of exponents:

(i) `a^-n = 1/(a^n)`

(ii) `a^(1/n) = rootn(a)`

Expression `= (16^(-1/4))^3`

Apply (i):

`= (1/(16^(1/4)))^3`

Apply (ii):

`= (1/root4(16))^3`

`= (1/2)^3`

`= 1/(2^3) = 1/8`