Question

Write (6x5y³)²/3x²y7 x 4xy-3 in the form axy where a, b and c are integers.

Answer 1

To simplify the expression (6x^5y^3)^2 / 3x^2y^7 x 4xy^-3 to axy form, we use exponent rules: power of a power, division and multiplication of exponents, resulting in the simplified form of 48x^9y^-4.

Step-by-step explanation:

We apply rules of exponents to simplify the expression (6x5y3)2 / 3x2y7 x 4xy-3 to the form axy where a, b and c are integers.

First, by the power of a power rule, we have:

(xa)b = xa.b

Applying this to (6x5y3)2:

62x5*2y3*2 = 36x10y6

Next, we divide by 3x2y7 and multiply by 4xy-3:

(36x10y6) / (3x2y7) = 12x8y-1
When we multiply that result with 4xy-3:

12x8y-1 × 4xy-3 = 48x9y-4

So, expressing in the form axy:

48x9y-4