1.What is the sum of the digits in the expanded form of the number 384cuberoot x5raised to the 20?What is 384cube root x5raised to the 20 in scientific notation?
If you mean ∛384 x 5^20
taking logs base 10,
log ∛384 = 1/3 log384 = 0.86144
log 5^20 = 20 log5 = 13.97940
add them to get the log of the product: 14.84084
10^0.84084 = 6.93170
so, ∛384 x 5^20 = 6.93170 x 10^14
No idea what you mean by "expanded form" of these numbers. The ∛ is irrational, so there is no end to the digits, hence no sum thereof.
Not sure how to add up the digits of 5^20 without just computing it, as you can do with any 15-digit calculator.
Thank you so much
To find the sum of the digits in the expanded form of 384cuberoot x5raised to the 20, we first need to simplify the expression.
The cube root of 384 can be written as the cube root of 64 multiplied by the cube root of 6. Since the cube root of 64 is 4, we can rewrite 384 as 4 * cube root of 6. So the expression becomes (4 * cube root of 6) multiplied by (5 raised to the power of 20).
Now, let's find the sum of the digits in the expanded form:
In the expression (4 * cube root of 6) * (5^20), we only have one digit, which is 6.
So the sum of the digits in the expanded form of the given expression is 6.
Now, moving on to the second part of the question, which asks for the expression 384cuberoot x5raised to the 20 in scientific notation:
To convert a number to scientific notation, we write it as a number between 1 and 10 multiplied by a power of 10.
In this case, we can rewrite 384cuberoot x5raised to the 20 as (4 * cube root of 6) * 10^20, since 384 is equivalent to 4 * 10^2 in scientific notation.
So, in scientific notation, 384cuberoot x5raised to the 20 can be written as (4 * cube root of 6) * 10^20.