(9/4)^-1

less than a minute read Jun 16, 2024
(9/4)^-1

Understanding (9/4)^-1

The expression (9/4)^-1 might seem intimidating at first, but it's actually quite simple to solve. Let's break down the concepts involved:

Understanding Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. In simpler terms:

x^-n = 1/x^n

Applying the Rule to (9/4)^-1

Using the rule above, we can rewrite (9/4)^-1 as:

(9/4)^-1 = 1 / (9/4)^1

Since any number raised to the power of 1 is itself, we have:

1 / (9/4)^1 = 1 / (9/4)

Dividing by a Fraction

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 9/4 is 4/9. Therefore:

1 / (9/4) = 1 * (4/9) = 4/9

Conclusion

Therefore, (9/4)^-1 is equal to 4/9.

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