Math Chapter 5

Question 1

Simplify (4x²)³.

Answer 1

The simplified expression is 64x⁶. Apply the rule of raising a power to a power: (a^m)ⁿ = a^{(m * n)}. Simplify: (4x²)³ = 4³ * (x²)³ = 64x⁶.

Question 2

Simplify (-5x)².

Answer 2

The simplified expression is 25x². Square the term: (-5x)² = (-5)² * (x)². Simplify: (-5)² = 25 and (x)² = x². Combine: 25x².

Question 3

Simplify -(-5x)².

Answer 3

The simplified expression is -25x². Square the term inside parentheses first: (-5x)² = 25x². Apply the negative outside: -25x².

Question 4

If the side length of a square is 3/2, what is its area?

Answer 4

The area of the square is 9/4 square units. Use the formula for area of a square: A = s². Substitute: A = (3/2)² = 9/4.

Question 5

A shelf is 26 inches long. If each textbook is 15/8 inches wide, how many books can fit on the shelf?

Answer 5

16 books can fit on the shelf. Set up the equation: 15/8 * n = 26. Solve for n: Multiply both sides by 8/15 (the reciprocal of 15/8): n = 26 * 8/15 = 16.

Question 6

Solve -14/25 k = 15/8.

Answer 6

k = -21/20. Multiply both sides by the reciprocal of -14/25, which is -25/14: k = (15/8) * (-25/14). Simplify: k = -21/20.

Question 7

Solve 4/5 m = 9/10.

Answer 7

m = 9/8 or 1 1/8 as a mixed number. Multiply both sides by the reciprocal of 4/5, which is 5/4: m = (9/10) * (5/4) = 9/8.

Question 8

Solve 5a = 1/7.

Answer 8

a = 1/35. Divide both sides by 5 or multiply by the reciprocal of 5, which is 1/5: a = (1/7) * (1/5) = 1/35.

Question 9

Solve n - 3/8 = 5/8.

Answer 9

n = 1. Add 3/8 to both sides: n = 5/8 + 3/8 = 8/8 = 1.

Question 10

Solve p - 1 3/5 = 2 4/5.

Answer 10

p = 3 17/20 or 3.85. Rewrite mixed numbers as improper fractions:
p - 8/5 = 14/5. Add 8/5 to both sides: p = 14/5 + 8/5 = 22/5 = 3 17/20.