You are given that x=4?

Question

You are given that x=4
Find values of:

(2x^-4)^3 * (x^4)^2

Answer 1

Well, x = 4 ---> x = 2^2

= (2* (2^2)^-4)^3 * ((2^2)^4)^2

Whenever powers are applied to other power expressions, you can multiply them:

= (2* 2^-8)^3 * ((2^8)^2)

Now, since you're multiplying a number times a power expression, since the number and the base of the power expression are the same, just increase the power by 1.

= (2^-7)^3 * (2^8)^2

= 2^-21 * 2^16

Multiplying two power expressions with the same base is equal to adding the powers themselves:

= 2^-5 = 1/32

Answer 2

You could try to substitute directly. That would give you
(2(4^(-4)))^3 . (4^4)^2
= (2 (1/256))^3 . (256)^2
= (1/128)^3 . (256)^2
= (1/2097152) . (65536)
= 1/32.

However, it's better to simplify it first:
(2x^-4)^3 . (x^4)^2
= (2^3) (x^(-4))^3 . (x^4)^2
= 8 x^(-12) . x^8
= 8 / x^4
= 8 / 4^4 (since x=4)
= 2^3 / 2^8
= 1/2^5
= 1/32.

Answer 3

When x=4
(2x^-4)^3 * (x^4)^2
=(2*4^-4)^3 * (4^4)^2
= [2* (1/(4^4))]^3*[256^2]
=[2/256]^3*256^2
= 2^3/256 = 8/256 = 1/32 = 2^-5

Also
x = 2^2, then
(2x^-4)^3 * (x^4)^2
= (2*(2^2)^-4)^3 * ((2^2)^4)^2
= (2*2^-8)^3 * 2^16 =2^-21*2^16=2^-5 = 1/32

Answer 4

2x^-4)^3 (x^4)^2
=(2/x^4)^3)(x^4)^2
with x=4, this is
=2/256)^3 (256)^2
=2/256
=1/128. ANS.

Answer 5

Substitute

(2x^-4)^3 * (x^4)^2 = (2(4)^-4)^3 * (4^4)^2

Answer 6

all you have to do is just substitute...