%5E-2.jpeg "(5/8)^-2")
Understanding (5/8)^-2
In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. Let's break down (5/8)^-2 step-by-step.
Applying the Rule of Negative Exponents
The rule for negative exponents states: x^-n = 1/x^n.
Therefore, (5/8)^-2 can be rewritten as:
(5/8)^-2 = 1/(5/8)^2
Simplifying the Expression
Now we need to calculate (5/8)^2:
(5/8)^2 = (5/8) * (5/8) = 25/64
Substituting this back into our expression:
1/(5/8)^2 = 1/(25/64)
Division of Fractions
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 25/64 is 64/25.
1/(25/64) = 1 * (64/25) = 64/25
Final Result
Therefore, (5/8)^-2 simplifies to 64/25.