Question

Find the values of A and B

(10x^3y^5)(4x²y^-2)/20x^-4y^B)^A=y^12/8x^27

a) A=3, B=7
b) A=4, B=9
c) A=5, B=5
d) A=6, B=3

Answer 1

The values of A and B are A=6 and B=3 (Option d). because The values of A and B (A=6, B=3) make the powers of x and y in the given expression equal, satisfying the equation.

Step-by-step explanation:

The given expression is:

`\[\frac{{10x^3y^5 \cdot 4x^2y^(-2)}}{{20x^(-4)y^B}^(A)} = \frac{{y^(12)}}{{8x^(27)}}\]`

To find the values of A and B, let's simplify the expression step by step.

First, combine the like terms in the numerator and denominator:

`\[\frac{{40x^5y^3}}{{20x^(-4)y^B}^(A)} = \frac{{y^(12)}}{{8x^(27)}}\]`

Now, simplify the powers:

`\[\frac{{40x^5y^3}}{{20x^(-4)y^B}^(A)} = \frac{{y^(12)}}{{8x^(27)}}\]`

To equate the powers of x and y on both sides, we get two equations:

`\[2 = 27 \implies x: A=6\]`

`\[3 - B = 12 \implies y: B=3\]`

Therefore, the correct values are A=6 and B=3, which corresponds to option d.

Therefore, the correct answer is option D