Answer:
[tex]343{x}^{6} {y}^{3}{z}^{3} [/tex]
Step-by-step explanation:
The given expresion is
[tex] {(7 {x}^{2}yz })^{3}[/tex]
We can rewrite this as:
[tex] {(7 {x}^{2}yz }) {(7 {x}^{2}yz }){(7 {x}^{2}yz })[/tex]
We regroup the terms to get;
[tex]7 \times 7 \times 7 \times {x}^{2} \times {x}^{2} \times {x}^{2} \times y \times y \times y \times z \times z \times z[/tex]
We apply the product rule of exponents.
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
According to this product rule, when the base is the same we write one base and add the exponents.
[tex] {7}^{1 + 1 + 1} \times {x}^{2 + 2 + 2} \times {y}^{1 + 1 + 1} \times {z}^{1 + 1 + 1} [/tex]
Simplify the exponents:
[tex]{7}^{3} {x}^{6} {y}^{3}{z}^{3} [/tex]
[tex]343{x}^{6} {y}^{3}{z}^{3} [/tex]
