%5E-1-as-a-fraction.jpeg "(3/5)^-1 As A Fraction")
Understanding (3/5)^-1 as a Fraction
In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. Let's break down how to express (3/5)^-1 as a fraction.
The Rule of Negative Exponents
The key rule to remember is: x^-n = 1/x^n
This means that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive version of the exponent.
Applying the Rule to (3/5)^-1
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Identify the base and exponent: In our example, the base is (3/5) and the exponent is -1.
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Apply the rule: Using the rule above, we can rewrite (3/5)^-1 as 1/(3/5)^1.
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Simplify: (3/5)^1 is simply 3/5. Therefore, 1/(3/5)^1 becomes 1/(3/5).
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Dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/5 is 5/3.
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Final result: So, 1/(3/5) is equivalent to 1 * (5/3), which equals 5/3.
Conclusion
Therefore, (3/5)^-1 expressed as a fraction is 5/3. Understanding the rule of negative exponents allows you to easily convert expressions with negative exponents into their fractional form.