Respuesta :
We have to simplify the expression here. The expression given,
[tex] (-5g^5h^6)^2(g^4h^2)^4 [/tex]
Now to find [tex] (-5g^5h^6)^2 [/tex] we will use power of a product property. We have to distribute the power here. We will get,
[tex] (-5g^5h^6)^2 = (-5)^2(g^5)^2(h^6)^2 [/tex]
= [tex] 25(g^5)^2(h^6)^2 [/tex]
Now we will use power of a power property. If given [tex] (a^m)^n [/tex] we will have to multtiply the powers and we will get [tex] a^{mn} [/tex]. So we will get here,
[tex] 25(g^5)^2(h^6)^2 = 25 g^{10} h^{12} [/tex]
Now the next part is [tex] (g^4h^2)^4 [/tex]
By using power of a power property we will get,
[tex] (g^4)^4(h^2)^4 = g^{16}h^8 [/tex]
Now we have to multiply them.
[tex] (25g^{10}h^{12} )(g^{16}h^8) [/tex]
Now we have to use product of powers property. If we have same base them we will have to add the exponents there. The formula is [tex] (a^m)(a^n) = a^{(m+n)} [/tex]. So we will get here,
[tex] 25(g^{10} g^{16})(h^{12} h^{8}) [/tex]
[tex] 25g^{(10+16)} h^{(12+8)} [/tex]
[tex] 25g^{26}h^{20} [/tex]
So we have got the required simplified answer here.
The simplified answer is [tex] 25g^{26}h^{20} [/tex].
