How to solve for zero exponents

Mathematics

1 answer:

Alexxx [7]4 years ago

8 0

if you have a zero exponent, the number (or the base) equals 1

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There are four large groups of people, each with 1000 members. any two of these groups have 100 members in common. any three of

Evgen [1.6K]

Let the groups be A, B, C and D. Then

n(A ∩ B ∩ C ∩ D) = 1
n(A ∩ B ∩ C ∩ D') = 10 - 1 = 9
n(A ∩ B ∩ C' ∩ D) = 10 - 1 = 9
n(A ∩ B' ∩ C ∩ D) = 10 - 1 = 9
n(A' ∩ B ∩ C ∩ D) = 10 - 1 = 9
n(A ∩ B ∩ C' ∩ D') = 100 - 9 - 9 - 1 = 81
n(A ∩ B' ∩ C ∩ D') = 100 - 9 - 9 - 1 = 81
n(A' ∩ B ∩ C ∩ D') = 100 - 9 - 9 - 1 = 81
n(A' ∩ B ∩ C' ∩ D) = 100 - 9 - 9 - 1 = 81
n(A' ∩ B' ∩ C ∩ D) = 100 - 9 - 9 - 1 = 81
n(A ∩ B' ∩ C' ∩ D) = 100 - 9 - 9 - 1 = 81
n(A ∩ B' ∩ C' ∩ D') = 1000 - 81 - 81 - 81 - 9 - 9 - 9 - 1 = 729
n(A' ∩ B ∩ C' ∩ D') = 1000 - 81 - 81 - 81 - 9 - 9 - 9 - 1 = 729
n(A' ∩ B' ∩ C ∩ D') = 1000 - 81 - 81 - 81 - 9 - 9 - 9 - 1 = 729
n(A' ∩ B' ∩ C' ∩ D) = 1000 - 81 - 81 - 81 - 9 - 9 - 9 - 1 = 729

Thus, all together there are 4(729) + 6(81) + 4(9) + 1 = 2,916 + 486 + 36 + 1 = 3,439 members in the groups.

Therefore, there are all together 3,439 members in the groups.

7 0

3 years ago

If the following fraction is reduced, what will be the exponent on the p? - 5p^5q^4/8p^2q^2 5 4 3 2

SSSSS [86.1K]

$\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad 
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------\\\\
-\cfrac{5p^5q^4}{8p^2q^2}\implies -\cfrac{5}{8}\cdot \cfrac{p^5q^4}{p^2q^2}\implies -\cfrac{5}{8}\cdot p^5p^{-2}q^4q^{-2}
\\\\\\
-\cfrac{5}{8}\cdot p^{5-2}q^{4-2}\implies -\cfrac{5\stackrel{\downarrow }{p^3}q^2}{8}$