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Pavel [41]
3 years ago
8

Evaluate the function can someone please explain how I would solve this please?

Mathematics
2 answers:
ElenaW [278]3 years ago
8 0
Y = 4 x 2^-6
y = 4 x 1/2^6
y = 4 x 1/64
y = 1/16
Elena-2011 [213]3 years ago
8 0
To think intuitively of what it means to take a number to a negative power, first consider how we define taking a number to a <em>positive </em>power.

Before we even get there, though, consider how we define multiplication as <em><span>repeated </span>addition</em>. When you see an expression like 3 x 5, what that essentially translates to is "add 3 to itself <em>5 times</em>," so we could also write 3 x 5 as 3 + 3 + 3 + 3 + 3. Having established that, around middle school, you'll typically get your first exposure to positive exponents, which are defined at first as <em>repeated multiplication</em>. When you see something like 3^5, we could also read that as "multiply 3 by itself <em>5 times</em>," or 3\times3\times3\times3\times3.

With that definition for <em>positive</em> exponents defined, it makes sense that we would define <em>negative </em>exponents in terms of the inverse of repeated multiplication: repeated <em>division</em>. Each time we step the exponent back by 1, we divide by the base again. For example, let's take these decreasing powers of 3 and notice what happens:

3^3 = 27\\3^2=27/3=9\\3^1=9/3=3\\3^0=3/3=1

If we start stepping back further, we start getting to values below 1:

3^{-1}=1/3\\3^{-2}=(1/3)/3=1/3^2=1/9\\ 3^{-3}=(1/9)/3=1/3^3=1/27

And this pattern continues, with the essential takeaway being that 3^{-x}=1/3^x

Try applying that pattern to the equation you've been given, y=4\cdot2^{-6}, and see what you get!
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