Solve and simplify this equation ^3 square root of 5 x 125 1/2. Show your work
To solve and simplify the equation ^3 √5 x 125 1/2, we need to calculate each term separately.
First, let's calculate the value of 125 1/2.
125 1/2 = (125)^(1/2) = √125 = 5√5
Now, let's put the values back into the equation:
^3 √5 x 125 1/2 = ^3 √5 x 5√5
To multiply these terms, we can simplify it further:
^3 √5 x 5√5 = ^3(5) x √(5) x √(5) = 15√(5) x √(5)
Using the property of radicals (√a x √b = √(ab)), we can simplify further:
15√(5) x √(5) = 15√(5) x √(5) = 15√(5)² = 15(5) = 75
Therefore, ^3 √5 x 125 1/2 simplifies to 75.
re-do the equation ^3 square root of 5 x 125 1/2 Show your work
To solve and simplify the equation ^3 √5 x 125 1/2, let's break it down step by step.
First, let's simplify 125 1/2.
125 1/2 = 125^(1/2) * 1/2^(1/2)
Now, let's calculate each term separately:
125^(1/2) = √125 = 5√5
1/2^(1/2) = √2/√2 = 1
Putting the values back into the equation:
^3 √5 x 125 1/2 = ^3 √5 x (5√5) * 1
Using the property of radicals (^a √b * ^c √d = ^a+c √(b*d)), we can simplify further:
^3 √5 x (5√5) * 1 = ^3+1 √(5*5) * 1 = ^4 √(25) * 1
Finally, simplifying:
^4 √(25) * 1 = ^4 √25 = √(25) = 5
Therefore, ^3 √5 x 125 1/2 simplifies to 5.
Re - Do and do not simplify the equation
To solve the equation ^3 √5 x 125 1/2 without simplifying, we can follow these steps:
First, let's break down the terms individually:
^3 √5 = 5^(1/3)
125 1/2 = (125)^(1/2) = √125 = 5√5
Now, let's put the values back into the equation:
^3 √5 x 125 1/2 = 5^(1/3) x 5√5
To multiply these terms, we can combine the bases:
5^(1/3) x 5√5 = 5^(1/3) x 5^(1/2) x √5
Using the multiplication rule of exponents (a^m * a^n = a^(m+n)), we can simplify further:
5^(1/3) x 5^(1/2) x √5 = 5^(1/3 + 1/2) x √5
Combining the exponents:
5^(1/3 + 1/2) x √5 = 5^(2/6 + 3/6) x √5 = 5^(5/6) x √5
Therefore, the equation ^3 √5 x 125 1/2, without simplifying, is 5^(5/6) x √5.