Questions: x^0=1, where x ≠ 0 When you raise (almost) anything to the power zero, you get 1. Here's the reason why this makes sense. Suppose I have 5^3/5^3, using the quotient rule this is 5^(3-3)=5^0. I can also think what happens when I simplify this like a fraction 5^3/5^3=125/125=1. x^0=x^n/x^n=1 as long as x isn't zero (we cannot divide by zero). Complete this expression. Assume that any variables are not equal to zero. z^0= Simplify the following expression completely. (4v+3)^0= Simplify the following. 2^0= Note: 0^0 is undefined. 0^n=0 for any exponent n ≠ 0. Simplify. 0^2=

$x^0=1, where x ≠ 0 When you raise (almost) anything to the power zero, you get 1. Here's the reason why this makes sense. Suppose I have 5^3/5^3, using the quotient rule this is 5^(3-3)=5^0. I can also think what happens when I simplify this like a fraction 5^3/5^3=125/125=1. x^0=x^n/x^n=1 as long as x isn't zero (we cannot divide by zero). Complete this expression. Assume that any variables are not equal to zero. z^0= Simplify the following expression completely. (4v+3)^0= Simplify the following. 2^0= Note: 0^0 is undefined. 0^n=0 for any exponent n ≠ 0. Simplify. 0^2=$

Transcript text: \[ x^{0}=1, \text { where } x \neq 0 \] When you raise (almost) anything to the power zero, you get 1 . Here's the reason why this makes sense. Suppose I have $\frac{5^{3}}{5^{3}}$, using the quotient rule this is $5^{3-3}=5^{0}$. I can also thing what happens when I simplify this like a fraction $\frac{5^{3}}{5^{3}}=\frac{125}{125}=1$. \[ x^{0}=\frac{x^{n}}{x^{n}}=1 \text { as long as } x \text { isn't zero (we cannot divide by zero). } \] Complete this expression. Assume that any variables are not equal to zero. \[ z^{0}= \] $\square$ Simplify the following expression completely. \[ (4 v+3)^{0}= \] $\square$ Simplify the following. \[ 2^{0}= \] $\square$ Note: $0^{0}$ is undefined. $0^{n}=0$ for any exponent $n \neq 0$. Simplify. $0^{2}=$ $\square$

Solution

Solution Steps

To solve the given expressions, we need to apply the property of exponents that states any non-zero number raised to the power of zero is equal to 1. This property is derived from the rules of exponents and division, as shown in the explanation. We will apply this rule to each expression.

For $ z^0 $, since $ z \neq 0 $, $ z^0 = 1 $.
For $ (4v + 3)^0 $, since the expression inside the parentheses is not zero, $ (4v + 3)^0 = 1 $.
For $ 2^0 $, since 2 is not zero, $ 2^0 = 1 $.

Step 1: Evaluate $ z^0 $

Given that $ z \neq 0 $, we apply the property of exponents: \[ z^0 = 1 \]

Step 2: Evaluate $ (4v + 3)^0 $

Since $ 4v + 3 \neq 0 $ for any non-zero $ v $, we have: \[ (4v + 3)^0 = 1 \]

Step 3: Evaluate $ 2^0 $

As $ 2 \neq 0 $, we find: \[ 2^0 = 1 \]