Please help me with the following(there is 9 problems so be prepared):
1.2^(1/3)∙4^(1/3)
I think it is 4 for the answer.
2. 11^(1/2)∙11^(1/2)
I think it is 11 for the answer.
3. 2^(1/2)∙2^(1/2)
I think it is 2 for the answer.
4. 3^(1/3)∙9^(1/3)
I think the answer is either 3 or 9.
5. 18^(1/2)∙18^(1/2)
I think the answer is 18.
6. 9^(-2.5)
I think the answer is 1/243.
7. 8^(4/3)
I think the answer is 16.
8. 20^(1/2)∙20^(1/2)
I think the answer is 20.
9. 27^(2/3)
I think the answer is 9.
I would appreciate it if any of you could help me. Thank you if you guys can help.
#1.
2^(1/3)*4^(1/3)
= 8^(1/3) = 2
#2,3 , ok
#4 same reasoning as #1
3((1/3) * 9^(1/3)
= 27(1/3) = 3
#5, 6, 7, 8, 9 are all ok
Thank you Reiny. I know it was a lot, so thank you for going through them and checking my answers. I will make sure to see what I did wrong on 1 and 4. Also, thank you for giving me another way of doing these type of problems. Thank you!
remember , the method I used only works if the exponents are the same,
that is,
a^m * b^m = (ab)^m
Sure, I can help you with these problems.
To solve these problems, we use the properties of exponents and the rules of multiplication.
1. To simplify 2^(1/3) ∙ 4^(1/3), we can rewrite 4 as 2^2 since 4 is equal to 2 raised to the power of 2. So the expression becomes 2^(1/3) ∙ 2^(2/3). According to the exponent rule, when you multiply two numbers with the same base, you add their exponents. So, in this case, 2^(1/3) ∙ 2^(2/3) simplifies to 2^[(1/3) + (2/3)] which is equal to 2^(3/3) which simplifies to 2^1 which is equal to 2. Therefore, the answer is 2.
2. To simplify 11^(1/2) ∙ 11^(1/2), we again use the exponent rule and add the exponents since the base is the same. So 11^(1/2) ∙ 11^(1/2) simplifies to 11^[(1/2) + (1/2)] which is equal to 11^1 which is equal to 11. Therefore, the answer is 11.
3. Similar to the previous problem, 2^(1/2) ∙ 2^(1/2) simplifies to 2^[(1/2) + (1/2)] which is equal to 2^1 which is equal to 2. So, the answer is 2.
4. To simplify 3^(1/3) ∙ 9^(1/3), we can again rewrite 9 as 3^2. So, the expression becomes 3^(1/3) ∙ 3^(2/3). According to the exponent rule, we add the exponents when multiplying two numbers with the same base. Therefore, 3^(1/3) ∙ 3^(2/3) simplifies to 3^[(1/3) + (2/3)] which is equal to 3^1 which is equal to 3. So, the answer is 3.
5. Similarly, 18^(1/2) ∙ 18^(1/2) simplifies to 18^[(1/2) + (1/2)] which is equal to 18^1 which is equal to 18. Therefore, the answer is 18.
6. To evaluate 9^(-2.5), we have a negative exponent. According to the exponent rule, any non-zero number raised to a negative power equals one divided by the number raised to the positive power. So, 9^(-2.5) is equivalent to 1 / 9^(2.5). We can rewrite 9^(2.5) as the square root of nine squared. Since the square root of nine is three, we have 1 / (3^2) which simplifies to 1 / 9. Therefore, the answer is 1/9.
7. To evaluate 8^(4/3), we raise 8 to the power of 4/3. This means taking the cube root of 8 (which is 2) and then raising it to the power of 4. So, 8^(4/3) is equivalent to 2^4 which is equal to 16. Therefore, the answer is 16.
8. Similarly, 20^(1/2) ∙ 20^(1/2) simplifies to 20^[(1/2) + (1/2)] which is equal to 20^1 which is equal to 20. Therefore, the answer is 20.
9. To evaluate 27^(2/3), we raise 27 to the power of 2/3. This means taking the cube root of 27 (which is 3) and then raising it to the power of 2. So, 27^(2/3) is equivalent to 3^2 which is equal to 9. Therefore, the answer is 9.
I hope this helps! Let me know if you have any further questions.