How would you solve this and could you give more examples?
(-e)^6f^1/e^6f^4
To solve the given expression (-e)^6f^1/e^6f^4, we can simplify it step by step.
Step 1: Apply the power rule for exponents.
(-e)^6f^1/e^6f^4 simplifies to (e^6f^1)/e^6f^4.
Step 2: Simplify the expression in the numerator.
The numerator is e^6f^1. Since the exponent is positive, we can leave it as it is.
Step 3: Simplify the expression in the denominator.
The denominator is e^6f^4. Since the exponent is positive, we can leave it as it is.
Step 4: Combine the numerator and denominator.
The simplified expression is (e^6f^1)/(e^6f^4).
Now, let's look at a similar example to illustrate the steps:
Example: Simplify (2x)^3/(2x^2)^2.
Step 1: Apply the power rule for exponents.
(2x)^3/(2x^2)^2 simplifies to (2^3x^3)/(2^2x^4).
Step 2: Simplify the expression in the numerator.
The numerator is 2^3x^3. Since the exponent is positive, we can leave it as it is.
Step 3: Simplify the expression in the denominator.
The denominator is 2^2x^4. Since the exponent is positive, we can leave it as it is.
Step 4: Combine the numerator and denominator.
The simplified expression is (2^3x^3)/(2^2x^4).
So, the general steps to solve expressions involving exponents are:
1. Apply the power rule for exponents.
2. Simplify the expression in the numerator and denominator separately.
3. Combine the numerator and denominator, if possible, into a single expression.
Remember to follow the order of operations if there are multiple operations involved in the expression.