Question
Simplify:
start fraction, 150, x, to the power 8 , y, to the power 4 , divided by, 25, x, to the power 6 , y, cubed, end fraction
25x
6
y
3
150x
8
y
4
Answer
Attempt 1 out of 2
Multiple Choice Answers
125, x, squared, y125x
2
y
6, x, to the power 14 , y, to the power 76x
14
y
7
125, x, to the power 14 , y, to the power 7125x
14
y
7
6, x, squared, y6x
2
y
start fraction, 150, x, to the power 8 , y, to the power 4 , divided by, 25, x, to the power 6 , y, cubed, end fraction
25x
6
y
3
150x
8
y
4
Answer
Attempt 1 out of 2
Multiple Choice Answers
125, x, squared, y125x
2
y
6, x, to the power 14 , y, to the power 76x
14
y
7
125, x, to the power 14 , y, to the power 7125x
14
y
7
6, x, squared, y6x
2
y
Answers
GPT-4o mini
To simplify the expression
\[
\frac{150x^8y^4}{25x^6y^3},
\]
we can start by simplifying the coefficients and then the variables.
1. **Coefficients**:
\[
\frac{150}{25} = 6.
\]
2. **Variables**:
For \(x\):
\[
\frac{x^8}{x^6} = x^{8-6} = x^2.
\]
For \(y\):
\[
\frac{y^4}{y^3} = y^{4-3} = y^1 = y.
\]
Now, combining these results, we get:
\[
6x^2y.
\]
Thus, the simplified expression is:
\[
6x^2y.
\]
From the provided multiple choice answers, it looks like the answer \(6x^2y\) is optioned, so that is the correct choice.
\[
\frac{150x^8y^4}{25x^6y^3},
\]
we can start by simplifying the coefficients and then the variables.
1. **Coefficients**:
\[
\frac{150}{25} = 6.
\]
2. **Variables**:
For \(x\):
\[
\frac{x^8}{x^6} = x^{8-6} = x^2.
\]
For \(y\):
\[
\frac{y^4}{y^3} = y^{4-3} = y^1 = y.
\]
Now, combining these results, we get:
\[
6x^2y.
\]
Thus, the simplified expression is:
\[
6x^2y.
\]
From the provided multiple choice answers, it looks like the answer \(6x^2y\) is optioned, so that is the correct choice.