Question
Solve the equation
n=1531575
Alternative Form
n≈0.775656
Evaluate
6n×9n×10n=252
Simplify
More Steps

Evaluate
6n×9n×10n
Rewrite the expression in exponential form
6n3×9×10
Multiply the terms
More Steps

Evaluate
6×9×10
Multiply the terms
54×10
Multiply the numbers
540
540n3
540n3=252
Divide both sides
540540n3=540252
Divide the numbers
n3=540252
Cancel out the common factor 36
n3=157
Take the 3-th root on both sides of the equation
3n3=3157
Calculate
n=3157
Solution
More Steps

Evaluate
3157
To take a root of a fraction,take the root of the numerator and denominator separately
31537
Multiply by the Conjugate
315×315237×3152
Simplify
315×315237×3225
Multiply the numbers
More Steps

Evaluate
37×3225
The product of roots with the same index is equal to the root of the product
37×225
Calculate the product
31575
315×315231575
Multiply the numbers
More Steps

Evaluate
315×3152
The product of roots with the same index is equal to the root of the product
315×152
Calculate the product
3153
Reduce the index of the radical and exponent with 3
15
1531575
n=1531575
Alternative Form
n≈0.775656
Show Solution
