Question

Please, need help

(Right answers only)

Answer 1

(1) Simplified expression:
`4 x^(2)`

(2) Simplified expression:
`-343 x^(3)`

(3) Simplified expression:
`45 x^(24)`

(4) Simplified expression:
`36x^(2)`

Solution:

(1) Original expression:
`(2 x)^(2)`

`(2 x)^(2)=2^2x^2=4x^2`

Simplified expression:
`4 x^(2)`

(2) Original expression:
`(-7 x)^(3)`

`(-7 x)^(3)=(-7)^3 x^3=-343x^3`

Simplified expression:
`-343 x^(3)`

(3) Original expression:
`5 x^(9) \cdot 3 x^(8) \cdot 3 x^(7)`

Multiply the numerical coefficients.

`(5\cdot 3\cdot 3) x^(9) \cdot x^(8) \cdot x^(7)`

If the bases are equal then the powers can add.

`45 x^(9+8+7)`

`45 x^(24)`

Simplified expression:
`45 x^(24)`

(4) Original expression:
`4(3 x)^(2)`

`4(3 x)^(2) =4 (3^2x^2)`

`=4\left(9 x^(2)\right)`

`=36x^(2)`

Simplified expression:
`36x^(2)`