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.

Question

asked Mar 21, 2021 79.6k views

1 Answer

Imus · Answer 1 · 2021-03-25T03:10:59+0000

Answer:

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

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:

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

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