Let's go through the step-by-step solutions for both questions.
## QUESTION 1
Simplify the expression: [tex]\(\frac{12 a^4 b}{3 a^3 b^2}\)[/tex]
1. First, simplify the numerical coefficients:
[tex]\[
\frac{12}{3} = 4
\][/tex]
2. Simplify the [tex]\(a\)[/tex] terms:
[tex]\[
\frac{a^4}{a^3} = a^{4-3} = a^1 = a
\][/tex]
3. Simplify the [tex]\(b\)[/tex] terms:
[tex]\[
\frac{b}{b^2} = b^{1-2} = b^{-1} = \frac{1}{b}
\][/tex]
Combining these results, we get:
[tex]\[
4 \cdot a \cdot \frac{1}{b} = \frac{4a}{b}
\][/tex]
So, the simplified expression [tex]\(\frac{12 a^4 b}{3 a^3 b^2}\)[/tex] is [tex]\(\boxed{\frac{4a}{b}}\)[/tex].
Correct answer: D. [tex]\(\frac{4 a}{b}\)[/tex]
## QUESTION 2
Simplify [tex]\(K^{-4}\)[/tex]
The property of exponents we use here is that [tex]\(x^{-n} = \frac{1}{x^n}\)[/tex].
Applying this property:
[tex]\[
K^{-4} = \frac{1}{K^4}
\][/tex]
So, [tex]\(K^{-4}\)[/tex] can be expressed as [tex]\(\boxed{\frac{1}{K^4}}\)[/tex].
Correct answer: D. [tex]\(\frac{1}{K^4}\)[/tex]
By following the steps methodically, we arrive at the correct answers for both questions.
