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)`.