Question

Simplify: [2]
(−3d'2e'4)'3
_________
9d'2e'5
" ' " is used for square..

Answer 1

`81 {d}^(4) {e}^(7)`

Explanation:

Use properties of degrees:

1. When multiplying different degrees on one term, the degree indicators must be multiplied, for example:

`( { {x}^(2)) }^(3) = {x}^(2 * 3) = {x}^(6)`

2. When dividing like terms (with the same base) with different degrees, the degree indicators must be subtracted, for example:

`\frac{ {x}^(5) }{ {x}^(2) } = {x}^(5 - 2) = {x}^(3)`

3. When squaring a negative term in parentheses, the minus is eliminated, for example:

`( { - 3x})^(2) = 9 {x}^(2)`

.

`\frac{ {(( { - 3d})^(2) * {e}^(4) )}^(3) }{ {9d}^(2) * {e}^(5) } = \frac{729 {d}^(6) * {e}^(12) }{9 {d}^(2) * {e}^(5) } = 81 {d}^(4) * {e}^(7)`