Final answer:
To simplify 3(4) ÷ 3(9), you divide by the common factor of 3, resulting in the simplified expression 4/9. When cubing exponentials, multiply the exponent by 3, and to eliminate terms and simplify, use the properties of exponents.
Step-by-step explanation:
To simplify the expression 3(4) ÷ 3(9), we need to divide both the numerator and the denominator by the common factor, which in this case is 3. The simplification process will look like this:
(3×4) ÷ (3×9) = (3/3) × (4) ÷ (3/3) × (9) = 4 ÷ 9
Simplifying further, 4 ÷ 9 cannot be simplified and so the simplified expression is 4/9.
When cubing of exponentials, you cube the coefficient as usual, and then multiply the exponent by 3. For example, if we have an expression like (2³)^2, we would cube 2 to get 8 and multiply the exponent by 3 to get a final answer of 2¹. This concept is helpful when simplifying expressions involving exponents.
To eliminate terms and simplify algebraic expressions, you should always look for common factors that can be divided out, and when dealing with exponents, use the properties of exponents to combine like terms (such as adding or subtracting exponents when multiplying or dividing the same base, respectively).