Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
r=−52325
Alternative Form
r≈−1.169607
Evaluate
r2×10r=−16
Multiply
More Steps
Evaluate
r2×10r
Multiply the terms with the same base by adding their exponents
r2+1×10
Add the numbers
r3×10
Use the commutative property to reorder the terms
10r3
10r3=−16
Divide both sides
1010r3=10−16
Divide the numbers
r3=10−16
Divide the numbers
More Steps
Evaluate
10−16
Cancel out the common factor 2
5−8
Use b−a=−ba=−ba to rewrite the fraction
−58
r3=−58
Take the 3-th root on both sides of the equation
3r3=3−58
Calculate
r=3−58
Solution
More Steps
Evaluate
3−58
An odd root of a negative radicand is always a negative
−358
To take a root of a fraction,take the root of the numerator and denominator separately
−3538
Simplify the radical expression
More Steps
Evaluate
38
Write the number in exponential form with the base of 2
323
Reduce the index of the radical and exponent with 3
2
−352
Multiply by the Conjugate
35×352−2352
Simplify
35×352−2325
Multiply the numbers
More Steps
Evaluate
35×352
The product of roots with the same index is equal to the root of the product
35×52
Calculate the product
353
Reduce the index of the radical and exponent with 3
5
5−2325
Calculate
−52325
r=−52325
Alternative Form
r≈−1.169607
Show Solution
Rewrite the equation
25x6+75x4y2+75x2y4+25y6=64
Evaluate
r2×10r=−16
Evaluate
More Steps
Evaluate
r2×10r
Multiply the terms with the same base by adding their exponents
r2+1×10
Add the numbers
r3×10
Use the commutative property to reorder the terms
10r3
10r3=−16
Divide both sides of the equation by 2
5r3=−8
Evaluate
5r2×r=−8
Evaluate
5(x2+y2)r=−8
Square both sides of the equation
(5(x2+y2)r)2=(−8)2
Evaluate
(5(x2+y2))2r2=(−8)2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
(5(x2+y2))2(x2+y2)=(−8)2
Use substitution
(25x4+50x2y2+25y4)(x2+y2)=(−8)2
Evaluate the power
(25x4+50x2y2+25y4)(x2+y2)=64
Solution
25x6+75x4y2+75x2y4+25y6=64
Show Solution
Graph
