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Answer :
Sure! Let's work through the division step-by-step.
We're trying to divide the expression [tex]\(-100 a^4 r^2 y\)[/tex] by [tex]\(\frac{1}{4} a r^2 y\)[/tex].
### Step 1: Setup the Division
Write the division of the given expressions:
[tex]\[
\frac{-100 a^4 r^2 y}{\frac{1}{4} a r^2 y}
\][/tex]
### Step 2: Work with Coefficients
First, handle the coefficients:
- The coefficient in the numerator is [tex]\(-100\)[/tex].
- The coefficient in the denominator is [tex]\(\frac{1}{4}\)[/tex].
To divide these, perform the calculation:
[tex]\[
-100 \div \left(\frac{1}{4}\right) = -100 \times 4 = -400
\][/tex]
### Step 3: Work with Variables
Now, deal with the variables [tex]\(a\)[/tex], [tex]\(r\)[/tex], and [tex]\(y\)[/tex]:
- For [tex]\(a\)[/tex]:
- In the numerator, it's [tex]\(a^4\)[/tex].
- In the denominator, it's [tex]\(a^1\)[/tex] (since [tex]\(a\)[/tex] is just [tex]\(a\)[/tex]).
Subtract the exponents: [tex]\(a^{4-1} = a^3\)[/tex].
- For [tex]\(r\)[/tex]:
- Both the numerator and denominator have [tex]\(r^2\)[/tex].
Subtract the exponents: [tex]\(r^{2-2} = r^0 = 1\)[/tex].
- For [tex]\(y\)[/tex]:
- Both the numerator and denominator have [tex]\(y^1\)[/tex].
Subtract the exponents: [tex]\(y^{1-1} = y^0 = 1\)[/tex].
### Step 4: Combine the Results
Combine the results from the coefficients and variables:
The expression becomes [tex]\(-400 a^3\)[/tex].
### Conclusion
So, the quotient of the division is [tex]\(-400 a^3\)[/tex]. Therefore, the correct option is (c) [tex]\(-400 a^3\)[/tex].
We're trying to divide the expression [tex]\(-100 a^4 r^2 y\)[/tex] by [tex]\(\frac{1}{4} a r^2 y\)[/tex].
### Step 1: Setup the Division
Write the division of the given expressions:
[tex]\[
\frac{-100 a^4 r^2 y}{\frac{1}{4} a r^2 y}
\][/tex]
### Step 2: Work with Coefficients
First, handle the coefficients:
- The coefficient in the numerator is [tex]\(-100\)[/tex].
- The coefficient in the denominator is [tex]\(\frac{1}{4}\)[/tex].
To divide these, perform the calculation:
[tex]\[
-100 \div \left(\frac{1}{4}\right) = -100 \times 4 = -400
\][/tex]
### Step 3: Work with Variables
Now, deal with the variables [tex]\(a\)[/tex], [tex]\(r\)[/tex], and [tex]\(y\)[/tex]:
- For [tex]\(a\)[/tex]:
- In the numerator, it's [tex]\(a^4\)[/tex].
- In the denominator, it's [tex]\(a^1\)[/tex] (since [tex]\(a\)[/tex] is just [tex]\(a\)[/tex]).
Subtract the exponents: [tex]\(a^{4-1} = a^3\)[/tex].
- For [tex]\(r\)[/tex]:
- Both the numerator and denominator have [tex]\(r^2\)[/tex].
Subtract the exponents: [tex]\(r^{2-2} = r^0 = 1\)[/tex].
- For [tex]\(y\)[/tex]:
- Both the numerator and denominator have [tex]\(y^1\)[/tex].
Subtract the exponents: [tex]\(y^{1-1} = y^0 = 1\)[/tex].
### Step 4: Combine the Results
Combine the results from the coefficients and variables:
The expression becomes [tex]\(-400 a^3\)[/tex].
### Conclusion
So, the quotient of the division is [tex]\(-400 a^3\)[/tex]. Therefore, the correct option is (c) [tex]\(-400 a^3\)[/tex].
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