Simplifying the Expression (1/4)^(-2)
When faced with an expression like (1/4)^(-2), it's important to understand the rules and principles of exponents and fractions in order to simplify it correctly. Let's break down the process step-by-step:
Step 1: Understand the Exponent
The exponent in this expression is -2. This means that we need to raise the base (1/4) to the power of -2. In other words, we need to find the reciprocal of (1/4) raised to the power of 2.
Step 2: Reciprocal of a Fraction
The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of 1/4 is 4/1 or simply 4.
Step 3: Raising a Fraction to a Power
When raising a fraction to a power, we can apply the following rule: (a/b)^n = a^n / b^n
In our case, we have (1/4)^(-2). Applying the rule, we get: (1/4)^(-2) = 1^(-2) / 4^(-2)
Step 4: Simplifying the Expression
Now, let's simplify the expression further: 1^(-2) = 1 4^(-2) = 1/16
Putting it all together, we get: (1/4)^(-2) = 1 / (1/16) = 16
Therefore, the simplified expression is 16.
In summary, to simplify the expression (1/4)^(-2), we need to:
- Understand the meaning of the negative exponent
- Find the reciprocal of the base (1/4)
- Apply the rule for raising a fraction to a power
- Simplify the resulting expression
By following these steps, you can easily simplify expressions involving fractions and negative exponents.