Final answer:
The product of 3x² and 9x⁴ is 27x⁶. This is found by multiplying the coefficients and adding the exponents of the 'x' variables, as per the exponent rule x^{p} × x^{q} = x^{p+q}.
Step-by-step explanation:
The student is asking for the product of two exponential expressions involving variables. To multiply 3x² by 9x⁴, we need to multiply the coefficients (the numbers in front of the variables) and add the exponents of the same base (in this case, 'x'). The exponent rules state that when multiplying two powers that have the same base, you can add the exponents. The coefficients 3 and 9 multiply to give 27. As for the variables, you add the exponents 2 and 4, because of the rule x^{p} × x^{q} = x^{p+q}. Therefore, the expression simplifies to 27x⁶.
An example of applying the rules for exponents to coefficients and powers of 10 can be found in the provided information. For instance, when multiplying powers of 10 such as 10² × 10³, the correct process is to add the exponents, giving us 10⁵. Similarly, when multiplying numerical coefficients, you should just multiply the numbers, such as 3.2 × 2 equals 6.4.