solve (24e)^1/3 / (3e)^1/3
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
Yah please don't write false titles or the like you might make people confused and they might not answer your wuestion right away. But anyway do the "e" mean exponent?
want to go out??
Writeacher, I think gav means e, the mathematical constant (2.71...)
since both numerator and denominator are raised by 1/3, we can group them up like so:
[(24e)/(3e)]^(1/3)
then simplify.. get it?
To simplify the expression (24e)^(1/3) / (3e)^(1/3), we can use the rules of exponents:
Step 1: First, let's simplify the numerator (24e)^(1/3).
To find the cube root of 24e, we can simplify the number and variable separately.
The cube root of 24 can be simplified as follows:
∛24 = ∛(8 * 3) = 2∛3
And the cube root of e remains the same.
Step 2: Next, let's simplify the denominator (3e)^(1/3).
Again, we can simplify the number and variable separately.
The cube root of 3 remains the same, and the cube root of e remains the same.
Step 3: Now, let's rewrite the simplified expression.
(24e)^(1/3) / (3e)^(1/3) can be written as:
(2∛3 * e) / (∛3 * e)
Step 4: Finally, we can simplify this expression further.
Since we have the same variable e in both the numerator and denominator, we can cancel them out:
(2∛3 * e) / (∛3 * e) = 2∛3 / ∛3
Step 5: To simplify the fraction further, we can rationalize the denominator.
Multiplying both the numerator and denominator by the conjugate of the denominator (∛3 + ∛3), we get:
(2∛3 / ∛3) * (∛3 + ∛3) / (∛3 + ∛3) = (2∛3 * (∛3 + ∛3)) / (∛3 * (∛3 + ∛3))
Expanding and simplifying the expression, we have:
(2∛3 * (∛3 + ∛3)) / (∛3 * (∛3 + ∛3)) = 2(∛3 * ∛3) / (∛3 * ∛3 + ∛3 * ∛3)
Since (∛3 * ∛3) equals 3, and (∛3 * ∛3 + ∛3 * ∛3) equals 2∛3 * ∛3, the expression simplifies to:
2(∛3 * ∛3) / (∛3 * ∛3 + ∛3 * ∛3) = 2 * 3 / (2∛3 * ∛3)
Further simplifying the expression, we get:
2 * 3 / (2∛3 * ∛3) = 6 / (2 * 3∛3)
Finally, canceling out the common factor of 2 in the numerator and denominator, we have:
6 / (2 * 3∛3) = 6 / (6∛3)
Therefore, the simplified expression of (24e)^(1/3) / (3e)^(1/3) is 1/∛3 or, equivalently, √3/3.