(6x^-2)^2(0.5x)^4
show work, symplify
To simplify the expression (6x^-2)^2(0.5x)^4, we can first simplify each term individually and then multiply them together.
For the first term, (6x^-2)^2, we can apply the exponent rule that states (a^m)^n = a^(m*n). Applying this rule, we have:
(6x^-2)^2 = 6^2 * (x^-2)^2
= 36 * x^(-2*2)
= 36 * x^-4
For the second term, (0.5x)^4, we can apply the exponent rule for products that states (ab)^n = a^n * b^n. Applying this rule, we have:
(0.5x)^4 = 0.5^4 * x^4
= 0.0625 * x^4
Now, we can multiply the two terms together:
(36 * x^-4) * (0.0625 * x^4)
= 36 * 0.0625 * x^-4 * x^4
= 2.25 * x^-4 * x^4
Applying the exponent rule that states x^m * x^n = x^(m+n), we have:
2.25 * x^-4 * x^4 = 2.25 * x^(-4+4)
= 2.25 * x^0
= 2.25
Therefore, the simplified expression is 2.25.