Question

Simplify the expression. (−5g5h6)2(g4h2)4

Answer 1

= 25*g^10 h^12 * g^16 h^8

= 25 g^26 h^20

Answer 2

We have to simplify the expression here. The expression given,

$(-5g^5h^6)^2(g^4h^2)^4$

Now to find $(-5g^5h^6)^2$ we will use power of a product property. We have to distribute the power here. We will get,

$(-5g^5h^6)^2 = (-5)^2(g^5)^2(h^6)^2$

= $25(g^5)^2(h^6)^2$

Now we will use power of a power property. If given $(a^m)^n$ we will have to multtiply the powers and we will get $a^{mn}$. So we will get here,

$25(g^5)^2(h^6)^2 = 25 g^{10} h^{12}$

Now the next part is $(g^4h^2)^4$

By using power of a power property we will get,

$(g^4)^4(h^2)^4 = g^{16}h^8$

Now we have to multiply them.

$(25g^{10}h^{12} )(g^{16}h^8)$

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 $(a^m)(a^n) = a^{(m+n)}$. So we will get here,

$25(g^{10} g^{16})(h^{12} h^{8})$

$25g^{(10+16)} h^{(12+8)}$

$25g^{26}h^{20}$

So we have got the required simplified answer here.

The simplified answer is $25g^{26}h^{20}$.