%5E-2-without-exponent.jpeg "(5/8)^-2 Without Exponent")
Understanding (5/8)^-2
The expression (5/8)^-2 might seem intimidating, but it's actually quite straightforward to understand and calculate. Let's break it down:
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. In other words:
x^-n = 1/x^n
Therefore, (5/8)^-2 is equivalent to 1/(5/8)^2.
Simplifying the Expression
Now, let's focus on (5/8)^2. This means multiplying (5/8) by itself:
(5/8)^2 = (5/8) * (5/8) = 25/64
Substituting back into our original expression:
1/(5/8)^2 = 1/(25/64)
Division by a Fraction
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 25/64 is 64/25. Therefore:
1/(25/64) = 1 * (64/25) = 64/25
Final Answer
Therefore, (5/8)^-2 simplified without exponents is 64/25.