Answer :
To solve the given problem and simplify the expression [tex]\( y = 5 \left( x^2 - 3 \right)^{-\frac{4}{5}} \)[/tex], we can rewrite the negative fractional exponent as a positive exponent in the denominator.
### Step-by-Step Solution:
1. Initial Expression:
Given:
[tex]\[ y = 5 \left( x^2 - 3 \right)^{-\frac{4}{5}} \][/tex]
2. Rewrite the Negative Exponent:
A negative exponent indicates a reciprocal. Therefore, we can rewrite the expression inside the exponential term by moving it to the denominator and making the exponent positive.
[tex]\[ y = 5 \cdot \frac{1}{\left( x^2 - 3 \right)^{\frac{4}{5}}} \][/tex]
3. Combine Terms:
By combining the terms, the expression simplifies to:
[tex]\[ y = \frac{5}{\left( x^2 - 3 \right)^{\frac{4}{5}}} \][/tex]
4. Final Simplified Expression:
The simplified form of the expression is:
[tex]\[ y = \frac{5}{(x^2 - 3)^{0.8}} \][/tex]
Hence, our final solution is:
[tex]\[ y = \frac{5}{(x^2 - 3)^{0.8}} \][/tex]
This is the simplified version of the given function [tex]\(y\)[/tex].
### Step-by-Step Solution:
1. Initial Expression:
Given:
[tex]\[ y = 5 \left( x^2 - 3 \right)^{-\frac{4}{5}} \][/tex]
2. Rewrite the Negative Exponent:
A negative exponent indicates a reciprocal. Therefore, we can rewrite the expression inside the exponential term by moving it to the denominator and making the exponent positive.
[tex]\[ y = 5 \cdot \frac{1}{\left( x^2 - 3 \right)^{\frac{4}{5}}} \][/tex]
3. Combine Terms:
By combining the terms, the expression simplifies to:
[tex]\[ y = \frac{5}{\left( x^2 - 3 \right)^{\frac{4}{5}}} \][/tex]
4. Final Simplified Expression:
The simplified form of the expression is:
[tex]\[ y = \frac{5}{(x^2 - 3)^{0.8}} \][/tex]
Hence, our final solution is:
[tex]\[ y = \frac{5}{(x^2 - 3)^{0.8}} \][/tex]
This is the simplified version of the given function [tex]\(y\)[/tex].
