Question
5 Problems - SHOW ALL WORK!
7^0=
rstu^0=
8^0m^0n=
t/4^0=
Why is anything to the zero power = 1 ?
7^0=
rstu^0=
8^0m^0n=
t/4^0=
Why is anything to the zero power = 1 ?
Answers
GPT 3.5
1) 7^0 = 1
We know that any number raised to the power of 0 is equal to 1. Therefore, 7^0 = 1.
2) rstu^0 = 1
Similarly, any variable raised to the power of 0 is also equal to 1. Therefore, rstu^0 = 1.
3) 8^0m^0n = 1
Using the product of powers property, we can combine the exponents:
8^0m^0n = (8^0)(m^0)(n) = 1 * 1 * n = n
Thus, 8^0m^0n simplifies to 1 * 1 * n = n.
4) t/4^0 = t
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 to 1. Therefore, t/4^0 is the same as t/1, which is equal to t.
Why is anything to the zero power = 1?
The rule that defines any number raised to the power of 0 as equal to 1 is a convention adopted in mathematics. It helps to simplify calculations and maintain consistency in algebraic expressions. The reasoning behind this convention can be understood using properties of exponents and the concept of division of powers. When a number is raised to the power of 0, it signifies that we are not actually multiplying by that number, but rather dividing by that number. And when we divide any number by itself, the result is always 1. Therefore, to maintain this consistency and convenience, we define any number raised to the power of 0 as equal to 1.
We know that any number raised to the power of 0 is equal to 1. Therefore, 7^0 = 1.
2) rstu^0 = 1
Similarly, any variable raised to the power of 0 is also equal to 1. Therefore, rstu^0 = 1.
3) 8^0m^0n = 1
Using the product of powers property, we can combine the exponents:
8^0m^0n = (8^0)(m^0)(n) = 1 * 1 * n = n
Thus, 8^0m^0n simplifies to 1 * 1 * n = n.
4) t/4^0 = t
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 to 1. Therefore, t/4^0 is the same as t/1, which is equal to t.
Why is anything to the zero power = 1?
The rule that defines any number raised to the power of 0 as equal to 1 is a convention adopted in mathematics. It helps to simplify calculations and maintain consistency in algebraic expressions. The reasoning behind this convention can be understood using properties of exponents and the concept of division of powers. When a number is raised to the power of 0, it signifies that we are not actually multiplying by that number, but rather dividing by that number. And when we divide any number by itself, the result is always 1. Therefore, to maintain this consistency and convenience, we define any number raised to the power of 0 as equal to 1.