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Which equation shows the correct use of the Power of Products Property?
A. (2x^5y^2)^3=6x^5y^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

Sagot :

naǫ
[tex](2x^5y^2)^3=2^3 \times (x^5)^3 \times (y^2)^3=8 \times x^{5 \times 3} \times y^{2 \times 3}=8x^{15}y^6[/tex]

The answer is D.

Answer:

Option D is correct.

[tex](2x^5y^2)^3= 8x^{15}y^6[/tex]

Step-by-step explanation:

Power of product property:

  • [tex](x^m)^n = x^{mn}[/tex]
  • [tex](ax)^m = a^m \cdot x^m[/tex]

Let the equation: [tex](2x^5y^2)^3[/tex]

Using power of products Property on given equation:

[tex](2x^5y^2)^3[/tex] = [tex]2^3 \cdot (x^5)^3 \cdot (y^2)^3 = 8 \cdot x^{15} \cdot y^6 = 8x^{15}y^6[/tex]

Therefore, the only option D of an equation which shows the correct use of power of Products property is,  [tex](2x^5y^2)^3= 8x^{15}y^6[/tex]


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