High School

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The area of a rectangle, given by [tex]A = l \cdot w[/tex], is represented by the expression [tex]24x^6 y^{15}[/tex]. Which could be the dimensions of the rectangle?

A. [tex]2x^5 y^8[/tex] and [tex]12x y^7[/tex]

B. [tex]6x^2 y^3[/tex] and [tex]4x^3 y^5[/tex]

C. [tex]10x^6 y^{15}[/tex] and [tex]14x^6 y^{15}[/tex]

D. [tex]9x^4 y^{11}[/tex] and [tex]12x^2 y^4[/tex]

Answer :

Answer:

A.

Step-by-step explanation:

so,

l × w = 24x⁶y¹⁵

remember,

a^b × a^c = a^(b+c)

A.

2x⁵y⁸ × 12xy⁷ = 2×12 × x⁵×x × y⁸×y⁷ = 24x⁶y¹⁵ correct

B.

6x²y³ × 4x³y⁵ = 6×4 × x²x³ × y³y⁵ = 24x⁵y⁸ incorrect

C.

10x⁶y¹⁵ × 14x⁶y¹⁵ = 10×14 × x⁶x⁶ × y¹⁵y¹⁵ = 140x¹²y³⁰ incorrect

D.

9x⁴y¹¹ × 12x²y⁴ = 9×12 × x⁴x² × y¹¹y⁴ = 108x⁶y¹⁵ incorrect

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