Write an expression with an exponent that is equvalent to 1/8
1/8 = 0.125
x^(0.125)
Or, do you mean
2^(-3) = 1/(2)^3 = 1/8
To write an expression with an exponent that is equivalent to 1/8, we need to apply the concept of fractional exponents. The exponent represents the power to which a base is raised. In this case, the base is not specified. However, we can find a base that will result in an exponent of 1/8.
To do this, we can use the property of exponents which states that if a number (base) raised to a power is equal to another number, then taking the reciprocal of the base and raising it to the reciprocal of the power will give us the desired result.
In this example, we want a base that, when raised to an exponent of 1/8, produces a value of 1. One way to achieve this is by using the number 1 as the base, because any number raised to the power of 0 equals 1. Therefore, raising 1 to any exponent will still equal 1.
Expression: (1^8)^((1/8)*(1/8))
Explanation:
Step 1: Start with the base 1.
Step 2: Raise the base to the power of 8: 1^8 = 1.
Step 3: Multiply the exponent by itself: (1/8) * (1/8) = 1/64.
Step 4: Raise the result of step 2 to the power of the exponent from step 3 to get the final answer: 1^(1/64) = 1.
Thus, the expression (1^8)^((1/8)*(1/8)) is equivalent to 1/8.