Final answer:
The expression 27 × 93x can be written as 3k where k is 3 + 6x. This utilizes the property that 27 is 33 and 9 is 32, allowing us to combine these exponents since the bases are the same.
Step-by-step explanation:
The student's question involves expressing the product of a numerical coefficient and an exponential term in the form of a single exponential expression with base 3. Specifically, the student wants to know how to write 27 × 93x as 3k, where k is an expression in terms of x.
To solve this, we can use the properties of exponents. First, recognize that both 27 and 9 are powers of 3: 27 is 33 and 9 is 32. The expression can then be transformed into a product of powers of 3:
- 27 × 93x = (33) × (32)3x
- Using the rule of exponents for multiplying exponential terms (am × an = am+n), we get:
- 33 × 36x = 33+6x
- The expression for k would be 3 + 6x, since it satisfies the condition 3k = 27 × 93x.
Thus, the value of k in the expression 3k is 3 + 6x, which represents the exponent of base 3 that equals to the product 27 × 93x.