Find the value of 2 to the power zero + 7 to the power 0 / 5 to the power 0
The correct answer and explanation is:
The expression is: 20+70502^0 + \frac{7^0}{5^0}
Let’s break this down step-by-step.
Step 1: Evaluating the Powers
In mathematics, any non-zero number raised to the power of zero is equal to 1. This rule applies to all numbers except zero itself.
So:
- 20=12^0 = 1
- 70=17^0 = 1
- 50=15^0 = 1
Step 2: Substituting the Values
Now substitute these values back into the original expression: 20+7050=1+112^0 + \frac{7^0}{5^0} = 1 + \frac{1}{1}
Step 3: Simplifying the Fraction
Since 11=1\frac{1}{1} = 1, the expression becomes: 1+1=21 + 1 = 2
Final Answer:
The value of the expression is 2\boxed{2}.
Explanation of the Concept
The exponentiation rule stating that any number raised to the power of zero equals 1 is a fundamental property in mathematics. This rule helps simplify many expressions and is critical in algebra, calculus, and other fields.
In the given problem, the powers of 2, 7, and 5 are all zero. As a result, the values of 202^0, 707^0, and 505^0 are each 1. The fraction 7050\frac{7^0}{5^0} simplifies to 11=1\frac{1}{1} = 1, so the entire expression simplifies to 1+1=21 + 1 = 2.
This is a simple example of how understanding the rules of exponents can help quickly evaluate expressions.