Question

question 1. in the expression shown, ( x ) is a positive real number. ( \frac{12x^9}{4x^{-2}} ) what is an equivalent form of this expression? move the correct answer to each box. each answer may be used more than once. not all answers will be used. ( square ) ( x ) ( square )

Explanation:

Step1: Simplify the coefficient

First, simplify the coefficient part of the fraction. We have \(\frac{12}{4}\).
\(\frac{12}{4} = 3\)

Step2: Simplify the variable part using exponent rules

For the variable part \(x^9\) divided by \(x^{-2}\), we use the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\). Here, \(a = x\), \(m = 9\) and \(n=- 2\). So we calculate the exponent: \(9-(-2)=9 + 2=11\). So the variable part simplifies to \(x^{11}\).

Step3: Combine the coefficient and variable part

Now, combine the simplified coefficient and the simplified variable part. The coefficient is \(3\) and the variable part is \(x^{11}\), so the expression becomes \(3x^{11}\).

Answer:

\(3x^{11}\) (assuming the boxes are for the coefficient and the exponent, so the first box is \(3\) and the second box is \(11\))