Question

Which expression is equivalent to 12a⁻⁴ b³c⁸/3a⁻² b⁹c⁻²

for all values of a, b, and c where the expression is defined?

Answer 1

To simplify the expression, we can use the laws of exponents:

12a⁻⁴ b³c⁸ / 3a⁻² b⁹c⁻²

= (12/3) (a⁻⁴ / a⁻²) (b³ / b⁹) (c⁸ / c⁻²)

= 4 (a⁻⁴+2) (b³-9) (c⁸+2)

= 4a⁻² b⁻⁶ c¹⁰

Therefore, the expression is equivalent to 4a⁻² b⁻⁶ c¹⁰ for all values of a, b, and c where the expression is defined.