To simplify the expression and write it in exponential form with positive exponents, we can use the laws of exponents.
The product of two numbers with the same base can be simplified by adding their exponents. So, we'll add the exponents of 2 that we have in this expression.
Now let's simplify step by step:
2^-7 * 2 * 2^-6
To combine the terms with the same base, we can add the exponents:
2^(-7+1-6)
Now, let's simplify the exponent:
2^-12
To write this in exponential form with positive exponents, we can take the reciprocal of the base with the positive exponent:
1/2^12
So, the fully simplified expression in exponential form with positive exponents is:
1/4096