%5E-4.jpeg "(1/3)^-4")
Understanding (1/3)^-4
The expression (1/3)^-4 might seem intimidating at first, but it's actually quite straightforward when we understand the rules of exponents. Let's break it down.
Negative Exponents
A negative exponent means we take the reciprocal of the base raised to the positive version of the exponent. In other words:
x^-n = 1 / x^n
Applying this to our problem:
(1/3)^-4 = 1 / (1/3)^4
Evaluating the Expression
Now we need to calculate (1/3)^4. This means multiplying (1/3) by itself four times:
(1/3)^4 = (1/3) * (1/3) * (1/3) * (1/3) = 1/81
Substituting back into our equation:
(1/3)^-4 = 1 / (1/81)
Finding the Reciprocal
Finally, we need to find the reciprocal of 1/81. The reciprocal of a fraction is simply flipping the numerator and denominator:
1 / (1/81) = 81/1 = 81
Conclusion
Therefore, (1/3)^-4 simplifies to 81.