Explain how you would fully simplify the expression below by naming the exponent law you would use, and state the operation you would perform on the exponents to simplify the expression. You must list the steps in the order they should be performed.
My teacher wants an explanation.
The expression is: (n^9n^-3)^-8/n^7
x^a * x^b = x^(a+b)
(x^a)^b = x^(ab)
now you can use those to calculate the correct power of n
(n^6)^-8/n^7
(n^(6 * -8) / n^7
n^-48 * n^-7
n^(-48-7)
n^-55
To simplify the expression (n^9n^-3)^-8/n^7, we can follow these steps:
Step 1: Apply the exponent law of multiplying same base exponents.
Since our base, n, is the same, we can multiply the exponents. This gives us (n^6)^-8/n^7.
Step 2: Apply the exponent law of raising a power to a power.
For (n^6)^-8, we can multiply the exponents. This gives us n^(-48)/n^7.
Step 3: Apply the exponent law of subtracting exponents when dividing.
Dividing n^(-48) by n^7, we can subtract the exponents. This gives us n^(-48-7).
Step 4: Simplify the expression.
Simplifying -48-7, we get -55. Therefore, our final expression is n^-55.
In summary, we used the exponent laws of multiplying same base exponents, raising a power to a power, and subtracting exponents when dividing to fully simplify the expression (n^9n^-3)^-8/n^7 to n^-55.