Fully simplify and write your answer in exponential form with positive exponents only.
z^-9\cdotz^-8=
Using the rules of exponents, we can simplify this expression as follows:
z^-9⋅z^-8 = z^(-9-8) = z^-17
Therefore, the fully simplified exponential form with positive exponents only is z^-17.
To simplify the expression z^-9 * z^-8, we can use the product of powers rule, which states that when multiplying two numbers with the same base, we add their exponents.
z^-9 * z^-8 = z^(-9 + -8)
Now, we can simplify the exponents by adding them:
z^(-9 + -8) = z^-17
To rewrite the answer in exponential form with positive exponents only, we can move the base with a negative exponent to the denominator:
z^-17 = 1/z^17
Therefore, z^-9 * z^-8 simplifies to 1/z^17.
To simplify the expression z^-9 * z^-8, we need to combine the terms with the same base, which in this case is z. To do that, we add the exponents. So, z^-9 * z^-8 can be written as z^(-9 + -8).
Now, to simplify the expression further, we simplify the exponent. (-9 + -8) equals -17. Therefore, z^(-9 + -8) can be written as z^-17 in exponential form.
However, we want the answer to be in exponential form with positive exponents only. Inverting an expression with a negative exponent gives us a positive exponent. So, we can rewrite z^-17 as 1/z^17.
Therefore, the fully simplified expression z^-9 * z^-8 can be written in exponential form with positive exponents only as 1/z^17.