x^a * x^b = x^(a+b)
(x^a)^b = x^(ab)
now you can use those to calculate the correct power of n
My teacher wants an explanation.
The expression is: (n^9n^-3)^-8/n^7
(x^a)^b = x^(ab)
now you can use those to calculate the correct power of n
(n^(6 * -8) / n^7
n^-48 * n^-7
n^(-48-7)
n^-55
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.