r^4 x r^-2 x r^-6
To simplify the expression r^4 x r^-2 x r^-6, we can combine the similar terms by adding the exponents:
r^(4 + (-2) + (-6))
Simplifying the exponents inside the parentheses:
r^(-4)
Therefore, r^4 x r^-2 x r^-6 simplifies to r^(-4).
To simplify the expression r^4 x r^-2 x r^-6, we can use the product rule of exponents which states that when multiplying terms with the same base, we can add their exponents.
First, let's rewrite the expression with the same base:
r^4 x r^-2 x r^-6 = r^(4 + (-2) + (-6))
Next, simplify the exponents:
r^(4 + (-2) + (-6)) = r^(-4)
Therefore, the simplified expression is r^(-4).
To simplify the expression r^4 x r^-2 x r^-6, we can use the properties of exponents.
First, let's apply the product rule, which states that when multiplying two exponential terms with the same base, you add their exponents. So we have:
r^4 x r^-2 = r^(4 + -2) = r^2
Next, let's multiply the result by r^-6 using the product rule again:
r^2 x r^-6 = r^(2 + -6) = r^-4
Therefore, the simplified expression of r^4 x r^-2 x r^-6 is r^-4.
If you want to understand this concept further, here's how you can calculate it step by step:
1. Start with the expression: r^4 x r^-2 x r^-6
2. Apply the rule for multiplying exponential terms with the same base: r^4 x r^-2 = r^(4 + -2) = r^2
3. Now, multiply the result by r^-6: r^2 x r^-6 = r^(2 + -6) = r^-4
Remember, when multiplying exponential terms with the same base, you add their exponents.