Solution: Algebra Homework on Simplifying Expressions and Exponents

This document presents a detailed solution to an algebra homework assignment, focusing on simplifying expressions and applying exponent rules. The assignment includes several sections: simplifying expressions with integer exponents, applying exponent rules, and problem-solving. Specific examples include simplifying expressions with single variables, multiple variables, and complex expressions involving parentheses and negative exponents. The problem-solving section addresses real-world applications, such as calculating areas using scientific notation. The document provides step-by-step solutions, demonstrating the application of exponent rules and algebraic manipulation techniques. The solution covers a wide range of algebraic concepts, providing a comprehensive guide for students studying algebra.

Exercise 7.3
Student Name
Institution
Date

Exercise 7.3
Guided practice
One; Simplify
1. 22∗23 =22+3=25
2. 53∗53=53 +3=56
3. n6∗n2=n6+2 =n8
4. x2∗x−3∗x 4=x2−3+4 =x−3
Two; Science
5. Speed 1000 m/hr
In 7.5∗105 hrs
You will travel
1000∗7.5∗105miles
which is 103∗7.5∗105=7.5∗108 miles
Three; Simplify
6. ( x2 )5
=x2∗5=x10
7. ( y4 )8
= y ( 4∗8 )= y32
8. ( p3 )3
=p3∗3= p9
9. ( 3−2 )2
=3−2∗2=3−4
10. ( a−3 )4
∗(a7 )2
=a−12∗a14 =a2
11. xy∗( x2 )3
∗( y3 )4
=xy∗x6∗y12=x7 y13
12. ( 2 t )5 =25∗t5=32 t5
13. ( 6 k ) 2=62∗k2=36 k 2
14. ( r2 s ) 7
=r14 s7
15. (−2 x5 )3
=(−23 x15)=0.125 x15
16. − ( 2 x5 )3
=− ( 23 x15 ) =−8 x15
17. ( a2 b2 )5
∗( a−5 )2
=a10 b10∗a−10=b10

Practice and problem solving
simplify
18. 32∗23∗3=23∗34
19. 6∗62∗63∗62=68
20. a5∗a0∗a−5=a0=1
21. x7∗x−6∗y−3=x y−3
22. Geography
Rhode Island Area 2.9∗1010 sq ft
Alaska area 5.5∗102∗Rhode area
Alaska is therefore
2.9∗1010∗5.5∗102=1.595∗1013