Question

Describe how you would use the rules of exponents to simplify (7x2yz)3. You may indicate an exponent in your answer with ^. For example, 3x2 y2as 3x^2y^2.

Answer 1

`343{x}^(6) {y}^(3){z}^(3)`

Explanation:

The given expresion is

`{(7 {x}^(2)yz })^(3)`

We can rewrite this as:

`{(7 {x}^(2)yz }) {(7 {x}^(2)yz }){(7 {x}^(2)yz })`

We regroup the terms to get;

`7 * 7 * 7 * {x}^(2) * {x}^(2) * {x}^(2) * y * y * y * z * z * z`

We apply the product rule of exponents.

`{a}^(m) * {a}^(n) = {a}^(m + n)`

According to this product rule, when the base is the same we write one base and add the exponents.

`{7}^(1 + 1 + 1) * {x}^(2 + 2 + 2) * {y}^(1 + 1 + 1) * {z}^(1 + 1 + 1)`

Simplify the exponents:

`{7}^(3) {x}^(6) {y}^(3){z}^(3)`

`343{x}^(6) {y}^(3){z}^(3)`