SOLUTION: What is z to the zero power times z to the negative 10th? Only using positive exponents.

Question 1190689: What is z to the zero power times z to the negative 10th? Only using positive exponents.
Found 2 solutions by math_tutor2020, Alan3354:
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Any nonzero number to the exponent of 0 will result in 1.
as long as
Multiplying by 1 has no effect, so the z^0 won't affect the answer.

The portion then turns into when we make the exponent positive. Take the reciprocal of the base to make the exponent positive.
The general rule is that or you can think of it like

Answer:

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
0^0 = 1, by convention.
========================
That means some people made that decision.
------------------
In 1752, Euler in Introductio in analysin infinitorum wrote that a0 = 1[15] and explicitly mentioned that 0^0 = 1.[16] An annotation attributed[17] to Mascheroni in a 1787 edition of Euler's book Institutiones calculi differentialis[18] offered the "justification"
{\displaystyle 0^{0}=(a-a)^{n-n}={\frac {(a-a)^{n}}{(a-a)^{n}}}=1}{\displaystyle 0^{0}=(a-a)^{n-n}={\frac {(a-a)^{n}}{(a-a)^{n}}}=1}
as well as another more involved justification. In the 1830s, Libri[19][17] published several further arguments attempting to justify the claim 0^0 = 1, though these were far from convincing, even by standards of rigor at the time.[20]
---------------
I wouldn't argue with Euler.
RELATED QUESTIONS
What is 3m to the negative 7th power divided by m to the negative 4th. Only using... (answered by ankor@dixie-net.com,ikleyn,josgarithmetic)
what is 3 to the power of 4 times 3 to the negative power of 7 finding the product only... (answered by Alan3354,ankor@dixie-net.com)
use answer using only positive exponents. 10 to the negative 2nd power multiplied by 10... (answered by robertb)
express using a positive exponent z raised to the negative fifth... (answered by piglet162431)
I know the answer to this problem, however I do not understand how to complete each step, (answered by josmiceli)
If a and b are real numbers and n is a positive integer, write a simplified expression... (answered by jsmallt9)
Use a combination of rules for exponents to simplify the expression. Give your answer in... (answered by checkley75)
what is the answer to 5z-3 over Z-1 times 5over z to 2nd... (answered by Fombitz)
what is 5 to the 10th... (answered by Stitch)