Question

Simplify and express each of the following in exponential form:
${2^0} + {3^0} + {4^0}$

Answer 1

To write the given expression in the exponential form, first simplify the expression by simplifying each of the terms with the help of the exponential property ${a^0} = 1$. Then the obtained result can be expressed in the required exponential form by using another exponential property $a = {a^1}$ .

Complete step by step solution:
If a number or any term is multiplied with itself for some number of times; then the expression which represents this repeated multiplication is called a power. For example, the repeated multiplication of 3 for two times can be shown as, $3 \times 3 = {3^2}$. The digit 3 is called the base and the number 2 is called the exponent.
The given expression is,
${2^0} + {3^0} + {4^0}$
To simplify and express the above expression in exponential form, use the exponent formula ${a^0} = 1$ .
The term ${2^0}$ can be written by using the property ${a^0} = 1$ as,
${2^0} = 1$
The term ${2^0}$can be written by using the property ${a^0} = 1$ as,
${3^0} = 1$
The term ${2^0}$ can be written by using the property ${a^0} = 1$ as,
${4^0} = 1$
Substitute 1 for 2 0 , 1 for 3 0 and 1 for 4 0 in the given expression ${2^0} + {3^0} + {4^0}$
and simplify.
${2^0} + {3^0} + {4^0} = 1 + 1 + 1 \\\ = 3 \\\$
Thus, the required simplified value of the given expression is 3.
Write the simplified value 3 in exponential form by using the exponential formula $a = {a^1}$
.$3 = {3^1}$
Hence, the required exponential form of the simplified value of the given expression is ${3^1}$.

Note:
In order to find the exponential form of the given expression we need to use the properties of exponentials that is, ${a^0} = 1$ and $a = {a^1}$ . These are the necessary properties which should be used to simplify the given expression.