Question

asked Apr 13, 2021 2.1k views

1 Answer

Subham Debnath · Answer 1 · 2021-04-18T09:25:37+0000

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:

(7x^2yz)^3=7^3(x^2)^3y^3z^3

Next, apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:

7^3(x^2)^3y^3z^3=7^3x^6y^3z^3

Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.

Therefore, the final result is:

343x^6y^3z^3

Step-by-step explanation:

The expression you have to simplify is:

(7x^2yz)^3

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:

$(abc)^z=a^z\cdot b^z\cdot c^z$

Using this with the expression
(7x^2yz)^3 it is:

$(7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3$

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:

(a^n)^m=a^(m* n)

You must apply that rule to the factor
(x^2)^3

That is:

(x^2)^3=x^((3* 2))=x^6

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:

(7x^2yz)^3=7^3(x^2)^3y^3z^3

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:

7^3(x^2)^3y^3z^3=7^3x^6y^3z^3

The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.

The final result is:
343x^6y^3z^3

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