Rewrite the expression as a product of identical factors to find the product for 100 exponent 3/2
. Submit your answer in simplified form.
To rewrite the expression as a product of identical factors, we need to find the factor that, when multiplied by itself multiple times, equals 100.
The square root of 100 is 10, so the factor that we need to multiply by itself multiple times is 10.
Therefore, the expression 100^(3/2) can be written as (10^2)^(3/2).
By applying the exponent rules, we can simplify this to 10^(2*(3/2)).
Now, let's simplify the exponent: 2*(3/2) = 3.
So, the product of 100^(3/2) is 10^3.
Therefore, 100^(3/2) = 10^3 = 1000.
thx lemme see if thats correct bot
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Rewrite the expression as a product of identical factors to simplify 125 exponent 2/3
. Submit your answer in simplified form. (1 point)
To rewrite the expression as a product of identical factors, we need to find the factor that, when multiplied by itself multiple times, equals 125.
The cube root of 125 is 5, so the factor that we need to multiply by itself multiple times is 5.
Therefore, the expression 125^(2/3) can be written as (5^3)^(2/3).
By applying the exponent rules, we can simplify this to 5^(3*(2/3)).
Now, let's simplify the exponent: 3*(2/3) = 2.
So, the product of 125^(2/3) is 5^2.
Therefore, 125^(2/3) = 5^2 = 25.
THX
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What rational number could be used as an exponent to rewrite 23−−√4
?(1 point)
To rewrite the expression 23√4 in exponential form, we need to find a rational number exponent that can be used.
Let's consider that the square root of 4 is 2, as √4 = 2.
So, 23√4 can be written as 23^2.
Therefore, the rational number exponent that can be used to rewrite 23√4 is 2.
What rational number could be used as an exponent to rewrite 23−−√exponent 4
?(1 point)
To rewrite the expression 23√4 with a rational number exponent, we need to find a rational number that, when raised to that power, results in 4.
The rational number exponent that can be used here is 1/2.
So, the expression 23√4 can be rewritten as 2^(1/2).
Therefore, the rational number that could be used as an exponent to rewrite 23√4 is 1/2.
How can you rewrite 9 exponent 1/3 using a root?(1 point)
To rewrite 9^(1/3) using a root, we can express it as the cube root of 9.
The cube root of a number, denoted as ∛, is the value that, when raised to the power of 3, equals that number.
So, 9^(1/3) can be rewritten as ∛9.
Therefore, you can rewrite 9^(1/3) using a root as the cube root of 9, which is denoted as ∛9.
What is the simplified form of 27 exponent 1/3?(1 point)
The simplified form of 27^(1/3) is the cube root of 27.
The cube root of 27 is 3, because 3 raised to the power of 3 equals 27.
Therefore, the simplified form of 27^(1/3) is 3.