%5E-1-without-exponents.jpeg "(9/8)^-1 Without Exponents")
Understanding (9/8)^-1 without exponents
The expression (9/8)^-1 might seem intimidating at first glance, especially if you're not comfortable with exponents. But fear not! We can rewrite this expression without using exponents and understand its meaning.
The Rule of Negative Exponents
The key to understanding this expression lies in the rule of negative exponents: a^-n = 1/a^n. This rule states that any number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive version of the exponent.
Applying the Rule to (9/8)^-1
Let's apply this rule to our expression:
(9/8)^-1 = 1/(9/8)^1
Now, any number raised to the power of 1 is simply itself. Therefore:
1/(9/8)^1 = 1/(9/8)
Dividing by a Fraction
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 9/8 is 8/9.
Therefore:
1/(9/8) = 1 * (8/9) = 8/9
Conclusion
We have successfully rewritten (9/8)^-1 without using exponents and found its equivalent value to be 8/9. Understanding the rules of exponents is crucial for simplifying mathematical expressions and solving various problems.