Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Timothy evaluated the expression using \( x = 3 \) and \( y = -4 \):

1. \(\left(\frac{1}{3}\right) x^{-1} y^2\)
2. \(\left(\frac{1}{3}\right) 3^{-1}(-4)^2\)
3. \(\left(\frac{1}{3}\right)\left(\frac{1}{3^1}\right)(-4)^2\)
4. \(\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)(-16)\)
5. \(-\frac{16}{9}\)

Analyze Timothy's steps. Is he correct? If not, why not?

A. Yes, he is correct.
B. No, he needed to add the exponents when he simplified the powers of the same base.
C. No, he needed to multiply 3 and -1 instead of creating a positive exponent in a fraction.
D. No, his value of [tex]\((-4)^2\)[/tex] should be positive because an even exponent indicates a positive value.

Sagot :

GinnyAnswer
Let's analyze Timothy's steps in detail to see if he correctly evaluated the expression given \( x = 3 \) and \( y = -4 \).

The expression to evaluate is: \(\left(\frac{1}{3}\right) x^{-1} y^2\).

Step-by-step solution:

1. Substitute \( x = 3 \) and \( y = -4 \) into the expression:
[tex]\[ \left(\frac{1}{3}\right) x^{-1} y^2 = \left(\frac{1}{3}\right) 3^{-1} (-4)^2 \][/tex]

2. Evaluate the powers:
- \( 3^{-1} = \frac{1}{3} \)
- \( (-4)^2 = 16 \)

So the expression becomes:
[tex]\[ \left(\frac{1}{3}\right) \left(\frac{1}{3}\right) \cdot 16 \][/tex]

3. Simplify the fractions and multiply:
[tex]\[ \left(\frac{1}{3}\right) \left(\frac{1}{3}\right) \cdot 16 = \frac{1}{3} \cdot \frac{1}{3} \cdot 16 = \frac{1}{9} \cdot 16 = \frac{16}{9} \][/tex]

4. Convert the fraction to a decimal:
[tex]\[ \frac{16}{9} \approx 1.7777777777777777 \][/tex]

So, the result of the evaluated expression is approximately \( 1.7777777777777777 \).

### Analysis of Timothy's Steps:

Let's consider each of Timothy's steps:

1. \(\left(\frac{1}{3}\right) x^{-1} y^2\)
2. \(\left(\frac{1}{3}\right) 3^{-1}(-4)^2\)
3. \(\left(\frac{1}{3}\right)\left(\frac{1}{3^1}\right)(-4)^2\)

These steps are correct so far.

4. \(\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)(-16)\)

Here, Timothy made a mistake. Evaluating \((-4)^2\) correctly should yield \(16\), not \(-16\).

Let's check the next suggestion in the question:
- No, his value of \( (-4)^2\) should be positive because an even exponent indicates a positive value.

This suggestion is correct. An even exponent makes the value positive, therefore:

Timothy's calculations were incorrect because the value of [tex]\( (-4)^2\)[/tex] should be positive 16.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.