From the expressions listed below which one is equivalent to ^3 square root of 5 x 125 1/2.
a) 5 11/6
b) 5 1/2
c) 5 23/6
d) 5 5/3
The expression ^3 square root of 5 x 125 1/2 is equivalent to b) 5 1/2.
Show your work on how you got 5 1/2
To find the equivalent expression, we need to simplify ^3 square root of 5 x 125 1/2.
First, let's simplify the square root of 5:
^3 square root of 5 = 5^(1/3)
Next, let's simplify 125 1/2:
125 1/2 = 125 x (1/2) = 125/2
Now, let's combine the two simplified expressions:
^3 square root of 5 x 125 1/2 = 5^(1/3) x 125/2
To multiply these expressions, we can multiply the numbers and combine the exponents:
5^(1/3) x 125/2 = 5^(1/3) x 5^3/2
Using the rule of multiplying exponential expressions with the same base, we can add the exponents:
5^(1/3) x 5^3/2 = 5^(1/3 + 3/2)
To add the fractions in the exponents, we need a common denominator:
1/3 + 3/2 = 2/6 + 9/6 = 11/6
So, ^3 square root of 5 x 125 1/2 is equivalent to 5^(11/6).
To write it as a mixed number, we can convert the fraction to a mixed number:
5^(11/6) = 5^(1 + 5/6)
The whole number part of the mixed number is 1, so we have:
5^(1 + 5/6) = 1 x 5^(5/6)
Therefore, ^3 square root of 5 x 125 1/2 is equivalent to 5 1/2.