What is the difference between positive and negative exponents

Mathematics

2 answers:

Sladkaya [172]4 years ago

5 0

Negative exponents create the reciprocal of the original number:

2^2=4
2^-2=1/4

4^4=64
4^-4=1/64

mrs_skeptik [129]4 years ago

5 0

Positive exponent means move the decimal to the right and it makes the number bigger and negative exponent means move the decimal to the left and it makes the number smaller. I hope this helped :D

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It’s been a while since I did Math but, in most scenarios, when you solve for an equation with only 1 x variable and you substit

patriot [66]

Let's replace every copy of x with 7 and simplify.

$\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\$

Which is clearly false. This is probably the set of steps you followed to get "no solution".

Why is there no solution? Well let's subtract 9 from both sides to isolate the square root

$\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\$

Recall that the result of a square root operation is never negative. The range of $y = \sqrt{x}$ and $y = \sqrt{5x+1}$ is the set of nonnegative numbers. There is no way we can have the left hand side result in -6