Final answer:
To solve for x in the equation 3^{2x} × 1/9 = 27, we apply the exponent rules and deduce that x = 2.5.
Step-by-step explanation:
To find the value of x in the equation 32x × 1⁄9 = 27, we can first rewrite the equation using the exponent rule provided, which states xP × xQ = x(P+Q). We are given that 1⁄9 is equivalent to 3-2, we can rewrite the equation as:
32x × 3-2 = 33
Using the rule xP × xQ = x(P+Q), we combine the exponents on the left side:
3(2x-2) = 33
Since the bases are the same, we can now equate the exponents:
2x - 2 = 3
Adding 2 to both sides we get:
2x = 5
Dividing both sides by 2, we find:
x = 2.5