Rewrite the expression as a product of identical factors to simplify 125 2/3
. Submit your answer in simplified form. (1 point)
125 2/3 can be rewritten as a product of identical factors by using the properties of exponents.
First, we can write 125 as 5^3, since 5*5*5 = 125.
Next, we can rewrite 2/3 as (2/3)^1 since any number raised to the power of 1 is still that number.
Therefore, 125 2/3 can be written as (5^3)(2/3)^1.
What rational number could be used as an exponent to rewrite 4√23
?
To rewrite 4√23 using a rational exponent, we can convert the radical notation to fractional exponent notation. The rational exponent that can be used is 2/4.
Since the index of the radical is 4, we can rewrite 4√23 as 23^(1/4)^2.
Simplifying the expression further, we have (23^(1/4))^2.
Thus, the rational number that can be used as an exponent to rewrite 4√23 is 2/4, which simplifies to 1/2.
How can you rewrite 9 1/3
using a root?
To rewrite 9 1/3 using a root, we can express it as a mixed number and then convert it to a fractional exponent.
First, we can express 9 1/3 as an improper fraction. To do this, we multiply the whole number (9) by the denominator (3) and add the numerator (1). This gives us (9 * 3 + 1) / 3 = 28/3.
Next, we can rewrite 28/3 using a fractional exponent. The denominator of 3 in the fraction represents the root, so we can write it as the 3rd root of 28 raised to the power of 1.
Therefore, 9 1/3 can be rewritten as the 3rd root of 28 raised to the power of 1, which is written as ∛28^1.
wrong
I apologize for the mistake. To rewrite 9 1/3 using a root, we can express it as a mixed number and then convert it to a fractional exponent.
First, we can express 9 1/3 as an improper fraction. To do this, we multiply the whole number (9) by the denominator (3) and add the numerator (1). This gives us (9 * 3 + 1) / 3 = 28/3.
Next, let's look for a root that gives us a whole number when applied to 28/3. Since the denominator is 3, we are looking for a root of the power 3.
We can rewrite 28/3 using a cube root. Therefore, 9 1/3 can be rewritten as the cube root of 28.
So, 9 1/3 can be rewritten as ∛28.
What is the simplified form of 27 1/3
?
To simplify 27 1/3, we can express it as an improper fraction and then rewrite it using exponent notation.
First, we can express 27 1/3 as an improper fraction. To do this, we multiply the whole number (27) by the denominator (3) and add the numerator (1). This gives us (27 * 3 + 1) / 3 = 82/3.
Next, we can rewrite 82/3 using exponent notation. The denominator of 3 in the fraction represents the root, so we can write it as the cube root of 82 raised to the power of 1.
Therefore, 27 1/3 can be simplified as the cube root of 82 raised to the power of 1, which is written as ∛82^1.
To rewrite the expression 125 2/3 as a product of identical factors, we need to convert the mixed number 125 2/3 to an improper fraction.
To do this, we multiply the whole number (125) by the denominator (3) and add the numerator (2) to get the new numerator:
125 * 3 + 2 = 375 + 2 = 377
Next, we place the new numerator (377) over the denominator (3) to get the improper fraction: 377/3.
Now, to express 377/3 as a product of identical factors, we need to find the prime factorization of the numerator (377) and the denominator (3).
The prime factorization of 377 is 13 * 29. These are both prime numbers, so we cannot simplify them further.
The prime factorization of 3 is simply 3, which is also a prime number.
Therefore, the expression 125 2/3 can be simplified as:
125 2/3 = (13 * 29) / 3
So, the answer in simplified form is: (13 * 29) / 3.