Question

Simplify. Your answer should be in simplest form with only positive exponents.

help me on 2,3,5​

Answer 1

2.
`g^(-2)` or
`(1)/(g^(2) )`. 3.
`8b^(5)` and 5.
`y^(4)`.

Explanation:

Step 1:

According to the product rule,
`(a^(x))(a^(y) ) = a^(xy)`

For question 2.
`g^(3) (g^(-5) )`,
`x=3`,
`y=-5,` and
`a=g.`

Substituting these values in the equation we get

`g^(3) (g^(-5) )`
`= g^(3-5) = g^(-2)`.

If the exponential is negative, it can be turned into a positive exponential by taking its reciprocal.

`g^(-2)= (1)/(g^(2) ).`

Step 2:

For question 3. The product rule is used again

`(4b^(2) )(2b^(3) )`,
`x=2`,
`y=3,` and
`a=b.`

Substituting these values in the equation we get

`(4b^(2) )(2b^(3) )`
`(8b^(2+3) = 8b^(5)`.

Step 3:

According to the division rule,
`(a^(x))/(a^(y))=a^(x-y)`

For question 5.
`(y^(6) )/(y^(2) )`,
`x=6`,
`y=6,` and
`a=y.`

Substituting we get
`(y^(6) )/(y^(2) ) = y^(6-2) = y^(4)`.