Could I have someone check my work please?
If I did something wrong please explain to me where I went wrong. Thank You.
Example of the product rule to solve would be, (5^3)(6^3)
Example of the quotient rule to solve would be, (4^2) / (8^2)
Example of the power rule to solve would be, (6^8)^8
I answered:
5^3 * 6^3 = (5*5*5) * (6*6*6) = 125 * 216 = 27,000
4^2 / 8^2 = (2*2)(2*2)/ (2*2*2)(2*2*2) = 2^4 / 2^6 = 2^-2 = 1/(2*2) = 1/4
(6^8)^8 = (6^8)(6^8)(6^8)(6^8)(6^8)(6^8)(6^8)(6^8) = 6^(8*8) = 6 ^64
Correct. :)
Thanks! =0)
Let's check your work step by step:
For the product rule problem, you correctly multiplied 5^3 and 6^3 to get (5*5*5) * (6*6*6) = 125 * 216 = 27,000. So, your answer of 27,000 is correct.
For the quotient rule problem, you correctly expanded 4^2 and 8^2 to get (2*2)(2*2)/ (2*2*2)(2*2*2). The next step would be to simplify the expression by canceling out common factors. In this case, note that both the numerator and denominator have 2^2. So, you can cancel them out and simplify further to get 2^4 / 2^6.
However, you made a mistake in the next step. When you divide 2^4 by 2^6, you should subtract the exponents: 2^4 / 2^6 = 2^(4-6) = 2^-2. This means the answer would be 1/(2^2), not 1/(2*2). Therefore, the correct answer for (4^2) / (8^2) is 1/4.
For the power rule problem, you correctly expanded (6^8)^8 into eight copies of 6^8. However, you made a mistake in the next step. When you multiply two exponents with the same base, you should add the exponents. So, instead of 6^(8*8), it should be 6^(8+8) = 6^16. Therefore, the correct answer for (6^8)^8 is 6^16.
Overall, you did a great job, but there was a small mistake in the quotient rule problem. Keep in mind the rule of subtracting exponents when dividing with the same base.