To solve the expression [tex]\( \frac{5 x^2 y z^9}{m^2 n^6 w^3} \)[/tex] in terms of the variables [tex]\( x \)[/tex], [tex]\( y \)[/tex], [tex]\( z \)[/tex], [tex]\( m \)[/tex], [tex]\( n \)[/tex], and [tex]\( w \)[/tex], follow these steps:
1. Understanding the Expression:
The given expression is composed of:
- A coefficient: [tex]\( 5 \)[/tex]
- Terms involving the variables [tex]\( x \)[/tex], [tex]\( y \)[/tex], [tex]\( z \)[/tex], [tex]\( m \)[/tex], [tex]\( n \)[/tex], and [tex]\( w \)[/tex].
- The variables are raised to certain powers and organized into a fraction.
2. Numerator:
The numerator of the given fraction is the product of:
- [tex]\( 5 \)[/tex]
- [tex]\( x^2 \)[/tex] (the variable [tex]\( x \)[/tex] squared)
- [tex]\( y \)[/tex] (the variable [tex]\( y \)[/tex])
- [tex]\( z^9 \)[/tex] (the variable [tex]\( z \)[/tex] raised to the ninth power)
So, the numerator is [tex]\( 5 \times x^2 \times y \times z^9 \)[/tex].
3. Denominator:
The denominator of the fraction is the product of:
- [tex]\( m^2 \)[/tex] (the variable [tex]\( m \)[/tex] squared)
- [tex]\( n^6 \)[/tex] (the variable [tex]\( n \)[/tex] raised to the sixth power)
- [tex]\( w^3 \)[/tex] (the variable [tex]\( w \)[/tex] cubed)
So, the denominator is [tex]\( m^2 \times n^6 \times w^3 \)[/tex].
4. Combining Numerator and Denominator:
The expression is thus the fraction with the numerator over the denominator:
[tex]\[
\frac{5 x^2 y z^9}{m^2 n^6 w^3}
\][/tex]
So, the simplified form of the given expression is [tex]\( \frac{5 x^2 y z^9}{m^2 n^6 w^3} \)[/tex].
