Certainly! Let's simplify each expression step-by-step.
### Expression 49:
[tex]\[
-d^4 e^{5 f^6} - d^4 e^{5 f} 6 + d^4 e^5 f^6
\][/tex]
To simplify this, first identify the common factor in all the terms:
Common Factor: [tex]\( d^4 \)[/tex]
Factoring out [tex]\( d^4 \)[/tex]:
[tex]\[
d^4 \left( -e^{5 f^6} - e^{5 f} 6 + e^5 f^6 \right)
\][/tex]
The terms in the parentheses cannot be further simplified since the exponents and bases are different. Thus, the simplified result is:
[tex]\[
-d^4 e^{5 f^6} - d^4 e^5 f^6 + d^4 e^{5 f} 6
\][/tex]
### Expression 50:
[tex]\[
-2 m^2 n^3 - 9 m^2 n^3 + 15 m^2 n^3
\][/tex]
Combine like terms:
[tex]\[
(-2 - 9 + 15) m^2 n^3
\][/tex]
Simplify the coefficients:
[tex]\[
4 m^2 n^3
\][/tex]
### Expression 51:
[tex]\[
-6 k^2 x^3 + 19 k^2 x^3 - 7 k^2 x^3
\][/tex]
Combine like terms:
[tex]\[
(-6 + 19 - 7) k^2 x^3
\][/tex]
Simplify the coefficients:
[tex]\[
6 k^2 x^3
\][/tex]
### Expression 52:
[tex]\[
-8 s^7 t^4 + 3 s^7 t^4 - 9 s^7 t^4
\][/tex]
Combine like terms:
[tex]\[
(-8 + 3 - 9) s^7 t^4
\][/tex]
Simplify the coefficients:
[tex]\[
-14 s^7 t^4
\][/tex]
### Final Simplified Results:
1. [tex]\( -d^4 e^{5 f^6} - d^4 e^5 f^6 + d^4 e^{5 f} 6 \)[/tex]
2. [tex]\( 4 m^2 n^3 \)[/tex]
3. [tex]\( 6 k^2 x^3 \)[/tex]
4. [tex]\( -14 s^7 t^4 \)[/tex]
