Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To simplify the expression [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex], let's follow these steps:
### Step 1: Understand the given expression
The expression we want to simplify is [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex].
### Step 2: Apply the properties of exponents
We know that:
[tex]\[ y^{-a} = \frac{1}{y^a} \][/tex]
Using this, we can rewrite [tex]\( y^{-2} \)[/tex] in the numerator:
[tex]\[ \frac{y^{-2}}{3 y^4} = \frac{1}{y^2} \cdot \frac{1}{3 y^4} \][/tex]
### Step 3: Combine the exponents
Since both terms involve [tex]\( y \)[/tex] with exponents, we can use the property of exponents which states:
[tex]\[ \frac{y^m}{y^n} = y^{m-n} \][/tex]
So:
[tex]\[ \frac{1}{y^2 \cdot 3 y^4} = \frac{1}{3 y^{2+4}} = \frac{1}{3 y^6} \][/tex]
### Step 4: Simplified expression
After combining the exponents and simplifying, we get:
[tex]\[ \frac{1}{3 y^6} \][/tex]
Hence, the simplified form of [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex] is [tex]\(\frac{1}{3 y^6}\)[/tex].
So, the correct choice from the given options is:
[tex]\[ \frac{1}{3 y^6} \][/tex]
### Step 1: Understand the given expression
The expression we want to simplify is [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex].
### Step 2: Apply the properties of exponents
We know that:
[tex]\[ y^{-a} = \frac{1}{y^a} \][/tex]
Using this, we can rewrite [tex]\( y^{-2} \)[/tex] in the numerator:
[tex]\[ \frac{y^{-2}}{3 y^4} = \frac{1}{y^2} \cdot \frac{1}{3 y^4} \][/tex]
### Step 3: Combine the exponents
Since both terms involve [tex]\( y \)[/tex] with exponents, we can use the property of exponents which states:
[tex]\[ \frac{y^m}{y^n} = y^{m-n} \][/tex]
So:
[tex]\[ \frac{1}{y^2 \cdot 3 y^4} = \frac{1}{3 y^{2+4}} = \frac{1}{3 y^6} \][/tex]
### Step 4: Simplified expression
After combining the exponents and simplifying, we get:
[tex]\[ \frac{1}{3 y^6} \][/tex]
Hence, the simplified form of [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex] is [tex]\(\frac{1}{3 y^6}\)[/tex].
So, the correct choice from the given options is:
[tex]\[ \frac{1}{3 y^6} \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.