UNIT TEST 2

1. What is the result when the quotient of [tex]4x^6[/tex] and [tex]-2x^2[/tex] is raised to the third power?
(1 mark)
Answer:

2. What is the 10th term in the pattern 1, 8, 27, 64 ...?
(1 mark)
Answer:

3. What algebraic expression represents the phrase below?
"Four times a number (x) more than twelve"
(1 mark)
Answer:



Answer :

Certainly! Let's tackle each question step by step.

### Question 1:
What is the result when the quotient of 4x^6 and -2x^2 is raised to the third power?

First, find the quotient of [tex]\(4x^6\)[/tex] and [tex]\(-2x^2\)[/tex]:

[tex]\[ \frac{4x^6}{-2x^2} = -2x^4 \][/tex]

Now, we need to raise this result to the third power:
[tex]\[ (-2x^4)^3 \][/tex]

Using exponential rules:
[tex]\[ (-2)^3 \cdot (x^4)^3 = -8 \cdot x^{12} \][/tex]

So, the answer is:
[tex]\[ \boxed{-8x^{12}} \][/tex]

### Question 2:
What is the 10th term in the pattern 1, 8, 27, 64 ...?

This sequence is a series of cubes:
[tex]\[ 1^3, 2^3, 3^3, 4^3, \ldots \][/tex]

Therefore, the 10th term is:
[tex]\[ 10^3 = 1000 \][/tex]

So, the 10th term is:
[tex]\[ \boxed{1000} \][/tex]

### Question 3:
What algebraic expression represents the phrase "Four times a number (x) more than twelve"?

The phrase translates directly into the algebraic expression as:
[tex]\[ 4x + 12 \][/tex]

So, the expression is:
[tex]\[ \boxed{4x + 12} \][/tex]

These answers fully address each part of the question.