Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
5 Hc. Is n' divisible by 20? Explain. H d. What is the least positive integer m so that 8,424 m is a perfect square?

5 Hc. Is n' divisible by 20? Explain. H d. What is the least positive integer m so that 8,424 m is a perfect square?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 21E: License Plate Numbers In the state of Pennsylvania, each standard automobile license plate number...
See similar textbooks
icon
Related questions
Question
100%

#38

c and d please

**Transcription for Educational Content:** **Divisibility Rules:** For an integer to be divisible by 3, the sum of its digits must be divisible by 3. For divisibility by 9, the sum of its digits must be divisible by 9. An integer is divisible by 5 if its right-most digit is 5 or 0. For divisibility by 4, the number formed by its right-most two digits must be divisible by 4. *Check the following integers for divisibility by 3, 4, 5, and 9:* a. 637,425,403,705,125 b. 12,858,306,120,312 c. 517,924,440,926,512 d. 14,328,083,360,232 **Unique Factorization Theorem:** 37. Use the unique factorization theorem to write the following integers in standard factored form. a. 1,176 b. 5,733 c. 3,675 38. Let \( n = 8,424 \). a. Write the prime factorization for \( n \). b. Write the prime factorization for \( n^5 \). c. Is \( n^5 \) divisible by 20? Explain. d. What is the least positive integer \( m \) so that 8,424\( \times m \) is a perfect square? 39. Suppose that in standard factored form \( a = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} \), where \( k \) is a positive integer; \( p_1, p_2, \ldots, p_k \) are prime numbers; and \( e_1, e_2, \ldots, e_k \) are positive integers. a. What is the standard factored form for \( a^3 \)? b. Find the least positive integer \( k \) such that \( 2^4 \cdot 3^5 \cdot 7 \cdot 11^2 \cdot k \) is a perfect cube (that is, it equals an integer to the third power). Write the resulting product as a perfect cube.
Transcribed Image Text:**Transcription for Educational Content:** **Divisibility Rules:** For an integer to be divisible by 3, the sum of its digits must be divisible by 3. For divisibility by 9, the sum of its digits must be divisible by 9. An integer is divisible by 5 if its right-most digit is 5 or 0. For divisibility by 4, the number formed by its right-most two digits must be divisible by 4. *Check the following integers for divisibility by 3, 4, 5, and 9:* a. 637,425,403,705,125 b. 12,858,306,120,312 c. 517,924,440,926,512 d. 14,328,083,360,232 **Unique Factorization Theorem:** 37. Use the unique factorization theorem to write the following integers in standard factored form. a. 1,176 b. 5,733 c. 3,675 38. Let \( n = 8,424 \). a. Write the prime factorization for \( n \). b. Write the prime factorization for \( n^5 \). c. Is \( n^5 \) divisible by 20? Explain. d. What is the least positive integer \( m \) so that 8,424\( \times m \) is a perfect square? 39. Suppose that in standard factored form \( a = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} \), where \( k \) is a positive integer; \( p_1, p_2, \ldots, p_k \) are prime numbers; and \( e_1, e_2, \ldots, e_k \) are positive integers. a. What is the standard factored form for \( a^3 \)? b. Find the least positive integer \( k \) such that \( 2^4 \cdot 3^5 \cdot 7 \cdot 11^2 \cdot k \) is a perfect cube (that is, it equals an integer to the third power). Write the resulting product as a perfect cube.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
SEE MORE TEXTBOOKS