Raising a Fractional Exponent: 1/8^-2
In this article, we will explore the properties of fractional exponents and evaluate the expression 1/8^-2.
What is a Fractional Exponent?
A fractional exponent is a power that is a fraction, such as 1/2, 1/3, or 2/3. It is used to indicate that a number should be raised to a power that is not an integer. For example, 2^(1/2) means "2 to the power of one-half," or the square root of 2.
The Rule of Negative Exponents
When a number is raised to a negative power, it means that the reciprocal of the number should be raised to the positive power. In other words:
a^(-n) = 1/a^n
For example, 2^(-3) = 1/2^3 = 1/8.
Evaluating 1/8^-2
Now, let's evaluate the expression 1/8^-2.
Using the rule of negative exponents, we can rewrite the expression as:
(1/8)^2
To evaluate this expression, we need to raise 1/8 to the power of 2.
(1/8)^2 = (1/8) × (1/8) = 64
So, 1/8^-2 is equal to 64.
Conclusion
In this article, we explored the properties of fractional exponents and evaluated the expression 1/8^-2. We used the rule of negative exponents to rewrite the expression and then raised 1/8 to the power of 2 to get the final answer, which is 64.
