Which equation shows the correct use of power of products property?
a) (2x^5y^2)^3 = 6x5y^2
b) (2x^5y^2)^3 = 6x^15y^6
c) (2x^5y^2)^3 = 8x^8y^5
d) (2x^5y^2)^3 = 8x^15y^6
Is it D? I am very counfused
To determine the correct equation that shows the use of the power of products property, we need to understand the concept of this property and apply it correctly.
The power of products property states that when raising a product to a power, you can distribute that power to each term inside the parentheses. In other words, you can raise each factor individually to the given power.
Let's examine each equation option:
a) (2x^5y^2)^3 = 6x5y^2
This equation is incorrect. The power of products property was not correctly applied. The power of 3 should be distributed to each term inside the parentheses.
b) (2x^5y^2)^3 = 6x^15y^6
This equation is incorrect. Although the power of 3 was correctly distributed to each term inside the parentheses, there is an error in the resulting exponents. The exponent of x should be 5 * 3 = 15, and the exponent of y should be 2 * 3 = 6.
c) (2x^5y^2)^3 = 8x^8y^5
This equation is incorrect. The resulting exponents are incorrect. The exponent of x should be 5 * 3 = 15, and the exponent of y should be 2 * 3 = 6.
d) (2x^5y^2)^3 = 8x^15y^6
This equation is correct. The power of products property was correctly applied. The exponent of 3 was distributed to each term inside the parentheses, resulting in x^5 raised to the power of 3 becoming x^15, and y^2 raised to the power of 3 becoming y^6. The coefficient 2 remains the same.
Therefore, the correct equation that shows the use of the power of products property is option d) (2x^5y^2)^3 = 8x^15y^6.
I hope this clarifies your confusion! Let me know if you have any further questions.
yes ... not to confused
everything gets raised to the power