Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Simplify:
(6x ^- 2)^2(0.5x)^4
I need some help, I'm pretty confused about this equation.

Answer 1

9/4

Explanation:

You want to simplify (6x^-2)^2(0.5x)^4.

Rules of exponents

The applicable rules of exponents are ...

(ab)^c = (a^c)(b^c)

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

Application

We first work out the value of each set of parentheses, then form the product of the results.

`(6x^(-2))^2(0.5x)^4=(6^2)(x^(-2\cdot2))(0.5^4)(x^4)=(36x^(-4))(1)/(16)x^4\\\\=(36)/(16)x^(-4+4)=\boxed{(9)/(4)}`

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Additional comment

As you know, x^0 = 1, so the variable disappears when this is simplified.