**Education Guide for Simplifying Exponential Expressions**Welcome to your guide on simplifying exponential expressions using only positive exponents.**Problem Statement:**Rewrite the following expression in the simplest form using only positive exponents:\[ \frac{(4^{-4})^{-3}}{4^{6}} \]**Solution Breakdown:**Below the problem, there are several dropdown selections. These are designed to break down the solution into smaller steps: 1. **The base in the answer is:** (Select one from the dropdown)2. **The exponent in the answer is:** (Select one from the dropdown)3. **The number in the numerator is:** (Select one from the dropdown)4. **The number in the denominator is:** (Select one from the dropdown)**Steps to solve:**1. Apply the power of a power rule: \((a^m)^n = a^{mn}\).2. Simplify the exponent.3. Subtract the exponent in the denominator from the exponent in the numerator.**Detailed Solution Explanation:**Given Expression: \[\frac{(4^{-4})^{-3}}{4^{6}}\]First, simplify the numerator using the power of a power rule:\[(4^{-4})^{-3} = 4^{(-4) \times (-3)} = 4^{12}\]Now, rewrite the original equation with the simplified numerator:\[\frac{4^{12}}{4^{6}}\]Next, use the quotient of powers rule \(\frac{a^m}{a^n} = a^{m-n}\):\[4^{12 - 6} = 4^6\]Thus, the simplified form using only positive exponents is:\[4^6\]To summarize:- **The base in the answer is:** 4- **The exponent in the answer is:** 6- **The number in the numerator is:** This step is not necessary after simplification.- **The number in the denominator is:** This step is not necessary after simplification.**Interactive Components:**This instructional example includes interactive dropdowns where students are supposed to select the correct numeral for each component of the simplified equation.Remember to always follow each exponent rule accurately to achieve the right solution!

Solution ) (44.4-2)/45 We know that am.an = am+n am/an = am-n We have = 4{4 +(-2)}/45 = 44 - 2/45 =…

POSSIBLE POINTS Rewrite the following expression in simplest form using only positive exponents. 4 The base in the answer is Select one the exponent in the answer is Select one the number in the numerator is Select one and the number in the denominator is Select one B

POSSIBLE POINTS Rewrite the following expression in simplest form using only positive exponents. 4 The base in the answer is Select one the exponent in the answer is Select one the number in the numerator is Select one and the number in the denominator is Select one B

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Education Guide for Simplifying Exponential Expressions**

Welcome to your guide on simplifying exponential expressions using only positive exponents.

**Problem Statement:**
Rewrite the following expression in the simplest form using only positive exponents:

\[ \frac{(4^{-4})^{-3}}{4^{6}} \]

**Solution Breakdown:**

Below the problem, there are several dropdown selections. These are designed to break down the solution into smaller steps:

1. **The base in the answer is:** (Select one from the dropdown)
2. **The exponent in the answer is:** (Select one from the dropdown)
3. **The number in the numerator is:** (Select one from the dropdown)
4. **The number in the denominator is:** (Select one from the dropdown)

**Steps to solve:**
1. Apply the power of a power rule: \((a^m)^n = a^{mn}\).
2. Simplify the exponent.
3. Subtract the exponent in the denominator from the exponent in the numerator.

**Detailed Solution Explanation:**
Given Expression: \[\frac{(4^{-4})^{-3}}{4^{6}}\]

First, simplify the numerator using the power of a power rule:
\[
(4^{-4})^{-3} = 4^{(-4) \times (-3)} = 4^{12}
\]

Now, rewrite the original equation with the simplified numerator:
\[
\frac{4^{12}}{4^{6}}
\]

Next, use the quotient of powers rule \(\frac{a^m}{a^n} = a^{m-n}\):
\[
4^{12 - 6} = 4^6
\]

Thus, the simplified form using only positive exponents is:
\[
4^6
\]

To summarize:
- **The base in the answer is:** 4
- **The exponent in the answer is:** 6
- **The number in the numerator is:** This step is not necessary after simplification.
- **The number in the denominator is:** This step is not necessary after simplification.

**Interactive Components:**
This instructional example includes interactive dropdowns where students are supposed to select the correct numeral for each component of the simplified equation.

Remember to always follow each exponent rule accurately to achieve the right solution!

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