Question

(3x)^2*x^-8/x^-12*4x^5

Answer 1

(9х^2*х^-8):4х^-7=9х^-6/4х^-7=9х/4

Answer 2

Let's simplify the expression step-by-step:

Step 1: Combine the exponents inside the parentheses. (3x)^2 = 3^2 * x^2 = 9x^2

Step 2: Apply the negative exponent rule for x^-8 and x^-12. x^-8 = 1/x^8 x^-12 = 1/x^12

Step 3: Combine the terms with x^5 and the terms with x^2, using the rules of exponents: (9x^2 * 1/x^8) / (1/x^12 * 4x^5)

Step 4: Simplify the expression further by dividing: (9x^2 * x^12) / (x^8 * 4x^5)

Step 5: Combine the exponents again: x^(2 + 12) / (x^8 * 4x^5)

Step 6: Simplify the exponents further: x^14 / (4x^13)

Step 7: Apply the rule of subtracting exponents when dividing like bases: x^(14 - 13) / 4

Step 8: Final result: x^1 / 4 or simply x/4

So, the simplified expression is (x/4).