Question

How would I simplify the expressions on the picture?

Answer 1

7.
`x^(11)` 8.
`y^(2)\\` 9.
`p^(12)` 10.
`a^(3) b^(2)` 11.
`g^(16)` 12.
`r^(9) h^(3)` 13.
`m^(15) p^(6)` 14.
`k^(6) y` 15.
`x^6 z^4`

Explanation:

7.
`x^3` ×
`x^8` =
`x^(11)` when multiplying with exponents you add

8.
`(y^(6) )/(y^(4) )` =
`y^(2)` when dividing with exponents you subtract

9.
`(p^(3))^4` =
`p^(12)\\` when it's power to power, you multiply

10.
`(a^(9) b^(4))/(a^(6) b^(2))` =
`a^(3) b^(2)` (subtract exponents)

11.
`(g^(8))^2` =
`g^(16)` (multiply exponents)

12.
`r^(4) h^(2) r^(5) h` =
`r^(9) h^(3)` (add exponents
`r^4 + r^5\\` and
`h^2 +h^1\\` )

13.
`(m^(5) p^(2))^3` =
`m^(15) p^(6)` (multiply exponents)

14.
`(k^(7) y^(4))/(y^(3)k)` =
`k^(6) y` (subtract exponents
`k^7-k^1` and
`y^4-y^3\\` )

15.
`x^3 z^2 x^3 z^2` =
`x^6 z^4` (add exponents same as #12)