What is the value of 8 to the power of 0?

What is the value of 8 to the power of 0?

• A. 0
• B. 1
• C. 8
• D. Infinity

Answer: (B)

The value of any non-zero number raised to the power of zero is defined to be 1. This is a fundamental property of exponents in mathematics. When you consider the expression \( a^n \), where \( a \) is any non-zero number and \( n \) is a positive integer, it follows that you can express \( a^n \) in terms of \( a^{n-1} \): \[ a^n = a \times a^{n-1} \] If you let \( n = 1 \), then: \[ a^1 = a \times a^0 \] To isolate \( a^0 \), you can rearrange this as follows: \[ a^0 = \frac{a^1}{a} \] As long as \( a \) is not zero, \( \frac{a}{a} = 1\). Hence, \( a^0 = 1\) regardless of the specific value of \( a \) (as long as it is non-zero). In this case, since you are calculating \( 8^0 \), and applying this rule, the result is 1. This property is useful and often

The value of any non-zero number raised to the power of zero is defined to be 1. This is a fundamental property of exponents in mathematics.

When you consider the expression ( a^n ), where ( a ) is any non-zero number and ( n ) is a positive integer, it follows that you can express ( a^n ) in terms of ( a^{n-1} ):

[

a^n = a \times a^{n-1}

]

If you let ( n = 1 ), then:

[

a^1 = a \times a^0

]

To isolate ( a^0 ), you can rearrange this as follows:

[

a^0 = \frac{a^1}{a}

]

As long as ( a ) is not zero, ( \frac{a}{a} = 1). Hence, ( a^0 = 1) regardless of the specific value of ( a ) (as long as it is non-zero).

In this case, since you are calculating ( 8^0 ), and applying this rule, the result is 1. This property is useful and often