Question

Simplify:

`(2x^-3)^4 (x^8)^(3/2)`

Answer 1

Let’s simplify:

`(2x^-3)^4 * (x^8)^(3/2)`

Step 1: Apply the power rule: `(ab)^n = a^nb^n and (x^m)^n = x^(mn)`

• `(2x^-3)^4 = 2^4 * x^(-3 - 4) = 16x^(-12)`
• `(x^8)^(3/2) = x^(8 * 3/2) = x^12`

Step 2: Multiply both expressions:

`16x^-12 * x^12`

= `16x^(-12 + 12)`

= `16x^0`

= 16