Find the cubic root of 189. (1 point)
3√7
9³√21
27³√7
3³√7
The correct answer is 3³√7
To find the cubic root of 189, you can use the exponentiation rule for roots:
1. Rewrite 189 as a product of prime factors: 189 = 3 * 3 * 3 * 7.
2. Divide the exponent of each prime factor by 3 since you're looking for the cubic root.
So, 189^(1/3) = (3^3 * 7)^(1/3).
3. Apply the exponentiation rule for roots by multiplying exponents:
189^(1/3) = 3^(3*(1/3)) * 7^(1/3).
4. Simplifying the exponent:
189^(1/3) = 3^1 * 7^(1/3).
Therefore, the cubic root of 189 is 3 * ³√7, which can be written as 3³√7.
To find the cubic root of 189, you need to identify the number that, when multiplied by itself three times, equals 189.
To check the given options:
1. 3√7: This option is not correct because it represents the square root of 7.
2. 9³√21: This option is also not correct because it includes the number 9 raised to the power of 3, and it does not involve the number 189.
3. 27³√7: This option is not correct either because it involves 27 raised to the power of 3 and it does not involve the number 189.
4. 3³√7: This option is the correct answer. When you raise 3 to the power of 3 and then take the cubic root of 7, you get the cubic root of 189.
So, the cubic root of 189 is represented by 3³√7.