(6x^-2)^2(0.5x)^4

Question

simplyfy, show work

Answer 1

We start by simplifying the expression $(6x^{-2})^2$. To do this, we square the coefficient 6 and square the base $x^{-2}$:

$(6x^{-2})^2 = 6^2(x^{-2})^2 = 36x^{-4}$

Next, we simplify the expression $(0.5x)^4$. To do this, we raise the coefficient 0.5 to the power of 4 and raise the base $x$ to the power of 4:

$(0.5x)^4 = 0.5^4x^4 = 0.0625x^4$

Now, we can multiply the two simplified expressions together:

$36x^{-4} \cdot 0.0625x^4 = 2.25x^{-4+4} = 2.25x^0$

Simplifying further, any non-zero number raised to the power of 0 is equal to 1, so $x^0 = 1$:

$2.25x^0 = 2.25(1) = 2.25$

Therefore, the simplified expression is 2.25.