Final answer:
To make the equation 81 x 9 = 801 true, we can reinterpret 81 as 8 x 10^1 and apply the given rule to manipulate the exponents, resulting in 8 x 10^2 + 1 = 801.
Step-by-step explanation:
To make the equation 81 x 9 = 801 true, we need to adjust one side to match the actual product of 81 and 9. Currently, 81 x 9 equals 729, not 801. To solve this problem, we can apply the rule given in your reference information:
xPx9 = x(p+q)
In this case, if x represents the number 8, p is the exponent we have on x, and q is the count of the number 9 following the dot operation, we can create the equivalence required. For this specific problem, 81 x 9 is similar to 8 x 101 x 9, which gives us 8 x 102, or 800. To achieve the value of 801, we can add 1 to the product.
Simple mathematical operations such as unit conversion can sometimes be applied to make sense of such problems. However, in this case, we are dealing with number properties and representations, not physical units, so unit conversion is not the appropriate method.
The rules of mathematics are universally valid and true regardless of the context, ensuring that we're applying them correctly.