Question
Simplify the expression
52000l5−433
Evaluate
8l×1×500l4×13−433
Solution
More Steps

Evaluate
8l×1×500l4×13
Rewrite the expression
8l×500l4×13
Multiply the terms
More Steps

Evaluate
8×500×13
Multiply the terms
4000×13
Multiply the numbers
52000
52000l×l4
Multiply the terms with the same base by adding their exponents
52000l1+4
Add the numbers
52000l5
52000l5−433
Show Solution

Find the roots
l=32505433×16254
Alternative Form
l≈0.383793
Evaluate
8l×1×500l4×13−433
To find the roots of the expression,set the expression equal to 0
8l×1×500l4×13−433=0
Multiply the terms
More Steps

Multiply the terms
8l×1×500l4×13
Rewrite the expression
8l×500l4×13
Multiply the terms
More Steps

Evaluate
8×500×13
Multiply the terms
4000×13
Multiply the numbers
52000
52000l×l4
Multiply the terms with the same base by adding their exponents
52000l1+4
Add the numbers
52000l5
52000l5−433=0
Move the constant to the right-hand side and change its sign
52000l5=0+433
Removing 0 doesn't change the value,so remove it from the expression
52000l5=433
Divide both sides
5200052000l5=52000433
Divide the numbers
l5=52000433
Take the 5-th root on both sides of the equation
5l5=552000433
Calculate
l=552000433
Solution
More Steps

Evaluate
552000433
To take a root of a fraction,take the root of the numerator and denominator separately
5520005433
Simplify the radical expression
More Steps

Evaluate
552000
Write the expression as a product where the root of one of the factors can be evaluated
532×1625
Write the number in exponential form with the base of 2
525×1625
The root of a product is equal to the product of the roots of each factor
525×51625
Reduce the index of the radical and exponent with 5
251625
2516255433
Multiply by the Conjugate
251625×5162545433×516254
The product of roots with the same index is equal to the root of the product
251625×5162545433×16254
Multiply the numbers
More Steps

Evaluate
251625×516254
Multiply the terms
2×1625
Multiply the terms
3250
32505433×16254
l=32505433×16254
Alternative Form
l≈0.383793
Show Solution
