Thank you for visiting Use the product rule to simplify each expression Write the results using exponents 31 tex x 2 cdot x 5 tex 32 tex y 2. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's go through each expression step-by-step and apply the product rule for exponents, which states that when you multiply two powers with the same base, you add the exponents.
31. [tex]\(x^2 \cdot x^5\)[/tex]
- Add the exponents: [tex]\(2 + 5 = 7\)[/tex]
- Result: [tex]\(x^7\)[/tex]
32. [tex]\(y^2 \cdot y\)[/tex]
- Remember [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex].
- Add the exponents: [tex]\(2 + 1 = 3\)[/tex]
- Result: [tex]\(y^3\)[/tex]
33. [tex]\((-3)^3 \cdot (-3)^9\)[/tex]
- The bases are the same, so add the exponents: [tex]\(3 + 9 = 12\)[/tex]
- Result: [tex]\((-3)^{12}\)[/tex]
34. [tex]\((-5)^7 \cdot (-5)^6\)[/tex]
- Add the exponents: [tex]\(7 + 6 = 13\)[/tex]
- Result: [tex]\((-5)^{13}\)[/tex]
35. [tex]\((5y^4)(3y)\)[/tex]
- Multiply the coefficients: [tex]\(5 \times 3 = 15\)[/tex]
- For the [tex]\(y\)[/tex] term: add the exponents: [tex]\(4 + 1 = 5\)[/tex]
- Result: [tex]\(15y^5\)[/tex]
36. [tex]\((-2z^3)(-2z^2)\)[/tex]
- Multiply the coefficients: [tex]\((-2) \times (-2) = 4\)[/tex]
- For the [tex]\(z\)[/tex] term: add the exponents: [tex]\(3 + 2 = 5\)[/tex]
- Result: [tex]\(4z^5\)[/tex]
37. [tex]\((x^9 y)(x^{10} y^5)\)[/tex]
- For the [tex]\(x\)[/tex] term: add the exponents: [tex]\(9 + 10 = 19\)[/tex]
- For the [tex]\(y\)[/tex] term: add the exponents: [tex]\(1 + 5 = 6\)[/tex]
- Result: [tex]\(x^{19} y^6\)[/tex]
38. [tex]\((a^2 b)(a^{13} b^{17})\)[/tex]
- For the [tex]\(a\)[/tex] term: add the exponents: [tex]\(2 + 13 = 15\)[/tex]
- For the [tex]\(b\)[/tex] term: add the exponents: [tex]\(1 + 17 = 18\)[/tex]
- Result: [tex]\(a^{15} b^{18}\)[/tex]
39. [tex]\((-8mn^6)(9m^2n^2)\)[/tex]
- Multiply the coefficients: [tex]\((-8) \times 9 = -72\)[/tex]
- For the [tex]\(m\)[/tex] term: add the exponents: [tex]\(1 + 2 = 3\)[/tex]
- For the [tex]\(n\)[/tex] term: add the exponents: [tex]\(6 + 2 = 8\)[/tex]
- Result: [tex]\(-72m^3n^8\)[/tex]
40. [tex]\((-7a^3b^3)(7a^{19}b)\)[/tex]
- Multiply the coefficients: [tex]\((-7) \times 7 = -49\)[/tex]
- For the [tex]\(a\)[/tex] term: add the exponents: [tex]\(3 + 19 = 22\)[/tex]
- For the [tex]\(b\)[/tex] term: add the exponents: [tex]\(3 + 1 = 4\)[/tex]
- Result: [tex]\(-49a^{22}b^4\)[/tex]
41. [tex]\((4z^{10})(-6z^7)(z^3)\)[/tex]
- Multiply the coefficients: [tex]\(4 \times (-6) \times 1 = -24\)[/tex]
- For the [tex]\(z\)[/tex] term: add the exponents: [tex]\(10 + 7 + 3 = 20\)[/tex]
- Result: [tex]\(-24z^{20}\)[/tex]
42. [tex]\((12x^5)(-x^6)(x^4)\)[/tex]
- Multiply the coefficients: [tex]\(12 \times (-1) \times 1 = -12\)[/tex]
- For the [tex]\(x\)[/tex] term: add the exponents: [tex]\(5 + 6 + 4 = 15\)[/tex]
- Result: [tex]\(-12x^{15}\)[/tex]
31. [tex]\(x^2 \cdot x^5\)[/tex]
- Add the exponents: [tex]\(2 + 5 = 7\)[/tex]
- Result: [tex]\(x^7\)[/tex]
32. [tex]\(y^2 \cdot y\)[/tex]
- Remember [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex].
- Add the exponents: [tex]\(2 + 1 = 3\)[/tex]
- Result: [tex]\(y^3\)[/tex]
33. [tex]\((-3)^3 \cdot (-3)^9\)[/tex]
- The bases are the same, so add the exponents: [tex]\(3 + 9 = 12\)[/tex]
- Result: [tex]\((-3)^{12}\)[/tex]
34. [tex]\((-5)^7 \cdot (-5)^6\)[/tex]
- Add the exponents: [tex]\(7 + 6 = 13\)[/tex]
- Result: [tex]\((-5)^{13}\)[/tex]
35. [tex]\((5y^4)(3y)\)[/tex]
- Multiply the coefficients: [tex]\(5 \times 3 = 15\)[/tex]
- For the [tex]\(y\)[/tex] term: add the exponents: [tex]\(4 + 1 = 5\)[/tex]
- Result: [tex]\(15y^5\)[/tex]
36. [tex]\((-2z^3)(-2z^2)\)[/tex]
- Multiply the coefficients: [tex]\((-2) \times (-2) = 4\)[/tex]
- For the [tex]\(z\)[/tex] term: add the exponents: [tex]\(3 + 2 = 5\)[/tex]
- Result: [tex]\(4z^5\)[/tex]
37. [tex]\((x^9 y)(x^{10} y^5)\)[/tex]
- For the [tex]\(x\)[/tex] term: add the exponents: [tex]\(9 + 10 = 19\)[/tex]
- For the [tex]\(y\)[/tex] term: add the exponents: [tex]\(1 + 5 = 6\)[/tex]
- Result: [tex]\(x^{19} y^6\)[/tex]
38. [tex]\((a^2 b)(a^{13} b^{17})\)[/tex]
- For the [tex]\(a\)[/tex] term: add the exponents: [tex]\(2 + 13 = 15\)[/tex]
- For the [tex]\(b\)[/tex] term: add the exponents: [tex]\(1 + 17 = 18\)[/tex]
- Result: [tex]\(a^{15} b^{18}\)[/tex]
39. [tex]\((-8mn^6)(9m^2n^2)\)[/tex]
- Multiply the coefficients: [tex]\((-8) \times 9 = -72\)[/tex]
- For the [tex]\(m\)[/tex] term: add the exponents: [tex]\(1 + 2 = 3\)[/tex]
- For the [tex]\(n\)[/tex] term: add the exponents: [tex]\(6 + 2 = 8\)[/tex]
- Result: [tex]\(-72m^3n^8\)[/tex]
40. [tex]\((-7a^3b^3)(7a^{19}b)\)[/tex]
- Multiply the coefficients: [tex]\((-7) \times 7 = -49\)[/tex]
- For the [tex]\(a\)[/tex] term: add the exponents: [tex]\(3 + 19 = 22\)[/tex]
- For the [tex]\(b\)[/tex] term: add the exponents: [tex]\(3 + 1 = 4\)[/tex]
- Result: [tex]\(-49a^{22}b^4\)[/tex]
41. [tex]\((4z^{10})(-6z^7)(z^3)\)[/tex]
- Multiply the coefficients: [tex]\(4 \times (-6) \times 1 = -24\)[/tex]
- For the [tex]\(z\)[/tex] term: add the exponents: [tex]\(10 + 7 + 3 = 20\)[/tex]
- Result: [tex]\(-24z^{20}\)[/tex]
42. [tex]\((12x^5)(-x^6)(x^4)\)[/tex]
- Multiply the coefficients: [tex]\(12 \times (-1) \times 1 = -12\)[/tex]
- For the [tex]\(x\)[/tex] term: add the exponents: [tex]\(5 + 6 + 4 = 15\)[/tex]
- Result: [tex]\(-12x^{15}\)[/tex]
Thank you for reading the article Use the product rule to simplify each expression Write the results using exponents 31 tex x 2 cdot x 5 tex 32 tex y 2. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
