Certainly! Let's solve the given expression step-by-step using the power of a quotient law.
The expression we need to simplify is:
[tex]\[ \left(\frac{a}{b}\right)^m \][/tex]
The power of a quotient law states that:
[tex]\[ \left(\frac{a}{b}\right)^m = \frac{a^m}{b^m} \][/tex]
Now let’s apply this law step-by-step:
1. Identify the numerator and denominator of the fraction inside the parentheses, which are [tex]\( a \)[/tex] and [tex]\( b \)[/tex], respectively.
2. Apply the exponent [tex]\( m \)[/tex] to both the numerator and the denominator separately. This means raising both [tex]\( a \)[/tex] and [tex]\( b \)[/tex] to the power [tex]\( m \)[/tex].
So, performing these operations, we get:
[tex]\[ \left(\frac{a}{b}\right)^m = \frac{a^m}{b^m} \][/tex]
We are given some specific values for [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( m \)[/tex]:
- [tex]\( a = \text{numerator} \)[/tex]
- [tex]\( b = \text{denominator} \)[/tex]
- [tex]\( m = 3 \)[/tex]
Substituting these values into our simplified expression, we get:
[tex]\[ \left(\frac{\text{numerator}}{\text{denominator}}\right)^3 = \frac{\text{numerator}^3}{\text{denominator}^3} \][/tex]
Therefore, the final result is:
[tex]\[ \left(\frac{\text{numerator}}{\text{denominator}}\right)^3 = \frac{\text{numerator}^3}{\text{denominator}^3} \][/tex]
This is the detailed step-by-step solution for the given question.
