(1/3)^-4

2 min read Jun 16, 2024
(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.

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