When you evaluate (1/8)^-1/3 answer will be
sorry.
(1/8)^(1/3) is 1/2
(1/8)^(-1/3) is 2
Apologies for the confusion in the previous response. You are correct.
To evaluate (1/8)^(-1/3), we can apply the rule that states when a negative exponent is raised to another exponent, the reciprocal of the base is taken and the absolute value of the exponent is used.
So, (1/8)^(-1/3) is the same as the reciprocal of (1/8)^(1/3).
Since (1/8)^(1/3) equals 1/2, the reciprocal of 1/2 is 2.
Therefore, the answer to (1/8)^(-1/3) is 2.
To evaluate the expression (1/8)^(-1/3), we follow the rules of exponentiation.
First, we note that a negative exponent represents the reciprocal of a number. So, we can rewrite the expression as:
(1/8)^(-1/3) = (8/1)^(1/3)
Next, we raise the base (8/1) to the power of the fractional exponent (1/3). The rule for raising a number to a fraction exponent can be represented as taking the nth root of the number, where n is the denominator of the fraction exponent.
In this case, the denominator of the fraction exponent is 3, so we take the cube root of (8/1):
(8/1)^(1/3) = ∛(8/1)
To simplify ∛(8/1), we figure out the cube root of 8. The cube root of 8 is 2 because 2 × 2 × 2 = 8.
So, ∛(8/1) = 2
Thus, the answer to the expression (1/8)^(-1/3) is 2.
To evaluate the expression (1/8)^(-1/3), you can use the property of a negative exponent, which states that (a^(-b)) equals 1 divided by (a^b).
Applying this property to the expression, we have:
(1/8)^(-1/3) = 1 / (1/8)^(1/3)
Now, let's simplify further by applying the exponent rule for the power of a power. The rule states that (a^b)^c is equal to a^(b*c).
(1/8)^(1/3) = (1^1/8^1)^(1/3) = 1^(1/3)/8^(1/3)
Since any number raised to the power of 1 is the number itself, we have:
1^(1/3)/8^(1/3) = 1/8^(1/3)
Now, we can express 8^(1/3) as the cube root of 8. The cube root of 8 is 2, as 2 * 2 * 2 = 8.
Therefore, 1/8^(1/3) = 1/2
So, the answer to the expression (1/8)^(-1/3) is 1/2.