anonymous
  • anonymous
Identify ALL true statements: 1. x^5 means 5(x) 2. 4^3 means to multiply 3 factors of 4 3. y^0=1 4. m^-1=-1m 5.3z^-2=(1)/(3z^2)
Mathematics
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
x^5 means you multiply 5 copies of x like this: x*x*x*x*x and it does NOT mean x times 5 or 5 times x
jim_thompson5910
  • jim_thompson5910
that's a very common misconception
jim_thompson5910
  • jim_thompson5910
so "x^5 means 5(x)" is false

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jim_thompson5910
  • jim_thompson5910
for #2, you apply the same logic 4^3 means you multiply 3 copies of 4: 4*4*4 and I guess saying "multiply 3 factors of 4" is a similar way to say it, so #2 looks true
anonymous
  • anonymous
For number 3 it would be 0 not 1 right?
jim_thompson5910
  • jim_thompson5910
actually no, another misconception but anything (except 0) to the 0th power is always 1
jim_thompson5910
  • jim_thompson5910
so y^0 = 1 is true
jim_thompson5910
  • jim_thompson5910
m^-1=-1m is false because it *should* be this m^-1 = 1/m
jim_thompson5910
  • jim_thompson5910
because x^(-k) = 1/(x^k)
jim_thompson5910
  • jim_thompson5910
so you can see how negative exponents and fractions tie together (and why the two aren't allowed in polynomials)
jim_thompson5910
  • jim_thompson5910
and finally 3z^-2=(1)/(3z^2) is false because the negative exponent only applies to the 'z'...so the 3 shouldn't be in the denominator and it should be this 3z^-2 = 3/(z^2)

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