Answer:
First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
Next, apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.
Therefore, the final result is:
[tex]343x^6y^3z^3[/tex]
Explanation:
The expression you have to simplify is:
[tex](7x^2yz)^3[/tex]
You have to apply two rules:
1. Power of a product
This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:
For instance:
[tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]
Using this with the expression [tex](7x^2yz)^3[/tex] it is:
[tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]
In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.
2. Power of a power:
This rule states that to raise a power to a power, you must multiply the exponents.
For instance:
[tex](a^n)^m=a^{m\times n}[/tex]
You must apply that rule to the factor [tex](x^2)^3[/tex]
That is:
[tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]
3. Final result and description using complete sentences:
The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.
The final result is: [tex]343x^6y^3z^3[/tex]
