Note: Your expression sounds a little unclear, so I am assuming your expression is
[tex]\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3[/tex]
But, the procedure to solve the expressions involving exponents remains the same, so whatever the expression is, you may be able to get your concept clear.
In the end, I will solve both expressions.
Answer:
Please check the explanation
Step-by-step explanation:
Given the expression
[tex]\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3[/tex]
solving the expression
[tex]\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}[/tex]
[tex]\left(y+1\right)^5\left(y+1\right)^3=\left(y+1\right)^{5+3}[/tex]
[tex]=\left(y+1\right)^8[/tex]
Therefore, we conclude that:
[tex]\left(y\:+\:1\right)^5\times \left(y\:+\:1\right)^3=\left(y+1\right)^8[/tex]
IF YOUR EXPRESSION IS THIS
↓
[tex]\left(y\:+\:1\right)^{\left(5y+1\right)^3}[/tex]
solving the expression
as
[tex]\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3[/tex]
so
[tex]\left(5y+1\right)^3=125y^3+75y^2+15y+1[/tex]
[tex]=125y^3+75y^2+15y+1[/tex]
Thus, the expression becomes
[tex]\left(y+1\right)^{\left(5y+1\right)^3}=\left(y+1\right)^{125y^3+75y^2+15y+1}[/tex]
