Answer:
9/4
Step-by-step 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.
[tex](6x^{-2})^2(0.5x)^4=(6^2)(x^{-2\cdot2})(0.5^4)(x^4)=(36x^{-4})\dfrac{1}{16}x^4\\\\=\dfrac{36}{16}x^{-4+4}=\boxed{\dfrac{9}{4}}[/tex]
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Additional comment
As you know, x^0 = 1, so the variable disappears when this is simplified.
