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2x to the power of -2
the answer is apparently 2 over x squared
explain this

User Qaphla
by
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1 Answer

1 vote

Answer:

See Below

Explanation:

When you have a negative exponent, you divide by the exponent hence the flipping. Here is an example to make it easier to explain. Below are some power of ten:


10^3=1000\\10^2=100\\10^1=10\\10^0 =1\\10^(-1)=(1)/(10) =(1)/(10^1) \\10^(-2)=(1)/(100) =(1)/(10^2)

When you go from an exponent to the one below it, you divide by the base. For example, to go from
10^3 to
10^2, you divide by ten. This is the same principle used to find the values of negative exponents.
10^0 is
10^1 divided by 10, so
10^(-1) should be
10^0 divided by ten.
10^0 is 1, making the value of
10^(-1) as
(1)/(10). When you divide by ten, you multiply by
(1)/(10), this effect makes the exponent stack on the bottom and correspond to the magnitude of the power.

For this specific example, we can write:


2x^(-2)

We are raising x to the power of negative 2, so we can say it is the same as
(1)/(x^2). We are also multiplying by 2, so that's how we get
(2)/(x^2)

If you need more of a visual, here are the powers of x:


x^2\\x^1=(x^2)/(x) \\x^0=(x^1)/(x)=1 \\x^(-1)=(1)/(x) \\x^(-2)=(x^(-1))/(x)=(1)/(x*x)=(1)/(x^2)

And we just multiply 2 times the value of
x^(-2).

Hope this helps.

User Jeremy Grozavescu
by
8.6k points

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