Problem-five properties of exponents

Question

Assignment:

Use the five properties of exponents to simplify each of the following expressions

Q1. (y⁵)³(y³)² / (y⁴)⁴

Find the values of each of the following polynomials for the given values of the variable.

Q2.  -x²  - 5x – 6, x = -3 and x = -2

Q3. What expressions raised to the fourth power is  81x¹²y⁸z¹⁶ ?

Q4. The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut.

Simplify each of the following expressions. Write your answer with positive exponents only.

Q5.  (x²)^-3(x^-2) / (x²)^-4

Perform the indicated calculations. Write your results in scientific notation.

Q6.  (6 x 10¹²)(3.2 x 10⁸) / (1.6 x 10⁷)(3 x 10²) 

Q7. The U.S. population in 1990 was approximately 250 million, and the average growth rate for the past 30 years gives a doubling time of 66 years. The formula for the United States is P(in millions) =  250 x 2^(y-1900)'/66. What will the population of the United States be in 2025, if this growth rate continues?

Q8. If there are 6 x 109 people on the Earth and there is enough freshwater to provide each person with 8.79 x 105 L, how much freshwater is on the Earth?

Q9. Add. 5b³ - 8b + 2b²  and 3b² - 7b³ + 5b 

Remove the parentheses in each of the following expressions and simplify when possible.

Q10.  8d – (-7c – 2d)

Q11. Subtract. 4x - 2x² + 4x³  from 4x³ + x - 3x²

Add using the vertical method.

Q12. 5x² + 2x - 4. x² - 2x - 3  and  2x² - 4x -3

Subtract using the vertical method.

Q13. 7x² + 6x  from  9x² - 3

Q14. A triangle has sides 3x + 7, 4x – 9, and 5x + 6. Find the polynomial that represents its perimeter.

Q15. Multiply.  8p²(2pq - 3p + 5q)

Q16. Multiply. (x-10) (x + 9)

Multiply, using the vertical method.

Q17.  (m² - 5mm + 3n²)(m² +4mm - 2n²)

Q18. (2r - 3s)(4r² + 6rs + 9s²) 

Q19. Multiply.  7w(2w - 3)(2w + 3)

Multiply the following.

Q20. (x / 3 + 3/ 4)(3x / 4 - 3 / 5)

Q21. The price of an item is given by p = 2x² - 100  Find the polynomial that represents the revenue generated from the sale of x items.

Find each of the following squares.

Q22. (7p + 6q)²

Q23. (w - 1/4)² 

Find each of the following products.

Q24. a(a + 5)(a - 5)

Let x represent the number and then write an expression for the product.

Q25. The square of 5 more than a number.

Q26. A square has sides of length 3x – 2 cm. Express the area of the square as a Polynomial.

Q27. Divide. 7x⁵y⁵ - 21x⁴y⁴ + 14x³y³ / 7x³y³

Q28. Perform the indicated divisions.  x²2x - 35 / x + 5

Q29. Perform the indicated divisions. 8x³ - 6x² + 2x / 4x + 1

Provide complete and step by step solution for the question and show calculations and use formulas.