What is the value of 3ypower zero

Mathematics

2 answers:

defon2 years ago

7 0

Answer:

Step-by-step explanation:

So anything to the power of zero is equal to 1. So you have the equation: $3y^0=3(1)=3$

If this doesn't make much sense, I sometimes like to use identities to show why this is. So since you're most likely learning exponents, you likely know the identity: $\frac{x^a}{x^b}=x^{a-b}$ well you can use this identity to express the equation: $\frac{x^a}{x^a}=x^{a-a}=x^0$ . and since x^a should equal x^a, and it's being divided by it self, this is equal to 1.

Btw if you didn't understand the identity: $\frac{x^a}{x^b}=x^{a-b}$ I'll try to briefly explain it. The reason this is true, is because you can cancel stuff out if it's being multiplied in the denominator and numerator. For example: $\frac{3a}{3}$ . I can cancel out the 3, because if I multiply 3 by a, and then divide by 3, I'm going to be left with a, because they're inverse to each other. This should hold true for exponents. So you can think of the identity more like: $\frac{x*x*x...\text{a amount of times}}{x*x*x\text{b amount of times}}$ seeing it like this might help understand why you subtract, since you're just cancelling out the x's.

I'll give you a more definitive example to help you grasp it in an example so: $\frac{2^4}{2^2}=\frac{2*2*2*2}{2*2}=\frac{2*2}{1}=2^2$ . See how I canceled out 2 of the 2's, well all I was really doing was subtracting 2 from the degree of the numerator, or in other words I was subtracting the degree of the denominator from the numerator since the bases were the same which is exactly what the identity is doing.