Question

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)

Answer 1

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

Answer 2

that's a very common misconception

Answer 3

so "x^5 means 5(x)" is false

Answer 4

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

Answer 5

For number 3 it would be 0 not 1 right?

Answer 6

actually no, another misconception but anything (except 0) to the 0th power is always 1

Answer 7

so y^0 = 1 is true

Answer 8

m^-1=-1m is false because it *should* be this m^-1 = 1/m

Answer 9

because

x^(-k) = 1/(x^k)

Answer 10

so you can see how negative exponents and fractions tie together (and why the two aren't allowed in polynomials)

Answer 11

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)