We appreciate your visit to Simplify each expression and match them to the correct answer a tex x 0 tex b tex 12x 3 2 tex c tex 2x 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's go through each problem step-by-step and simplify them:
a. [tex]$x^0$[/tex]
- Any number raised to the power of zero is equal to 1.
- Therefore, [tex]$x^0 = 1$[/tex].
- Answer: 1
b. [tex]$\left(12x^3\right)^2$[/tex]
- When you have a power of a product, raise each factor to the power.
- [tex]$= 12^2 \cdot (x^3)^2$[/tex]
- [tex]$= 144 \cdot x^{3 \cdot 2}$[/tex]
- [tex]$= 144x^6$[/tex]
- Answer: [tex]$144x^6$[/tex]
c. [tex]$2x^{-2}$[/tex]
- A negative exponent means take the reciprocal of the base.
- [tex]$= \frac{2}{x^2}$[/tex]
- Answer: [tex]$\frac{2}{x^2}$[/tex]
d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex]
- Multiply the coefficients and add the exponents of like bases.
- Coefficient: [tex]$12 \cdot (-5) = -60$[/tex]
- Exponents: [tex]$x^{2+3} = x^5$[/tex]
- So, [tex]$12x^2 \cdot (-5x^3) = -60x^5$[/tex]
- Answer: [tex]$-60x^5$[/tex]
e. [tex]$\frac{8x^{10}}{2x^2}$[/tex]
- Divide the coefficients and subtract the exponents of like bases.
- Coefficient: [tex]$\frac{8}{2} = 4$[/tex]
- Exponents: [tex]$x^{10-2} = x^8$[/tex]
- So, [tex]$\frac{8x^{10}}{2x^2} = 4x^8$[/tex]
- Answer: [tex]$4x^8$[/tex]
Now, let's match these simplified expressions to the given answers:
1. [tex]$4x^8$[/tex] matches e. [tex]$\frac{8x^{10}}{2x^2}$[/tex]
2. [tex]$\frac{2}{x^2}$[/tex] matches c. [tex]$2x^{-2}$[/tex]
3. 1 matches a. [tex]$x^0$[/tex]
4. [tex]$-60x^5$[/tex] matches d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex]
5. [tex]$144x^6$[/tex] matches b. [tex]$\left(12x^3\right)^2$[/tex]
Therefore, the correct matches are:
- a. [tex]$x^0$[/tex] → 3. 1
- b. [tex]$\left(12x^3\right)^2$[/tex] → 5. [tex]$144x^6$[/tex]
- c. [tex]$2x^{-2}$[/tex] → 2. [tex]$\frac{2}{x^2}$[/tex]
- d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex] → 4. [tex]$-60x^5$[/tex]
- e. [tex]$\frac{8x^{10}}{2x^2}$[/tex] → 1. [tex]$4x^8$[/tex]
a. [tex]$x^0$[/tex]
- Any number raised to the power of zero is equal to 1.
- Therefore, [tex]$x^0 = 1$[/tex].
- Answer: 1
b. [tex]$\left(12x^3\right)^2$[/tex]
- When you have a power of a product, raise each factor to the power.
- [tex]$= 12^2 \cdot (x^3)^2$[/tex]
- [tex]$= 144 \cdot x^{3 \cdot 2}$[/tex]
- [tex]$= 144x^6$[/tex]
- Answer: [tex]$144x^6$[/tex]
c. [tex]$2x^{-2}$[/tex]
- A negative exponent means take the reciprocal of the base.
- [tex]$= \frac{2}{x^2}$[/tex]
- Answer: [tex]$\frac{2}{x^2}$[/tex]
d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex]
- Multiply the coefficients and add the exponents of like bases.
- Coefficient: [tex]$12 \cdot (-5) = -60$[/tex]
- Exponents: [tex]$x^{2+3} = x^5$[/tex]
- So, [tex]$12x^2 \cdot (-5x^3) = -60x^5$[/tex]
- Answer: [tex]$-60x^5$[/tex]
e. [tex]$\frac{8x^{10}}{2x^2}$[/tex]
- Divide the coefficients and subtract the exponents of like bases.
- Coefficient: [tex]$\frac{8}{2} = 4$[/tex]
- Exponents: [tex]$x^{10-2} = x^8$[/tex]
- So, [tex]$\frac{8x^{10}}{2x^2} = 4x^8$[/tex]
- Answer: [tex]$4x^8$[/tex]
Now, let's match these simplified expressions to the given answers:
1. [tex]$4x^8$[/tex] matches e. [tex]$\frac{8x^{10}}{2x^2}$[/tex]
2. [tex]$\frac{2}{x^2}$[/tex] matches c. [tex]$2x^{-2}$[/tex]
3. 1 matches a. [tex]$x^0$[/tex]
4. [tex]$-60x^5$[/tex] matches d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex]
5. [tex]$144x^6$[/tex] matches b. [tex]$\left(12x^3\right)^2$[/tex]
Therefore, the correct matches are:
- a. [tex]$x^0$[/tex] → 3. 1
- b. [tex]$\left(12x^3\right)^2$[/tex] → 5. [tex]$144x^6$[/tex]
- c. [tex]$2x^{-2}$[/tex] → 2. [tex]$\frac{2}{x^2}$[/tex]
- d. [tex]$12x^2 \cdot \left(-5x^3\right)$[/tex] → 4. [tex]$-60x^5$[/tex]
- e. [tex]$\frac{8x^{10}}{2x^2}$[/tex] → 1. [tex]$4x^8$[/tex]
Thanks for taking the time to read Simplify each expression and match them to the correct answer a tex x 0 tex b tex 12x 3 2 tex c tex 2x 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
