Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−135y3−4374
Evaluate
−y2×135y−4374
Solution
More Steps
Evaluate
−y2×135y
Multiply the terms with the same base by adding their exponents
−y2+1×135
Add the numbers
−y3×135
Use the commutative property to reorder the terms
−135y3
−135y3−4374
Show Solution
Factor the expression
−27(5y3+162)
Evaluate
−y2×135y−4374
Multiply
More Steps
Evaluate
y2×135y
Multiply the terms with the same base by adding their exponents
y2+1×135
Add the numbers
y3×135
Use the commutative property to reorder the terms
135y3
−135y3−4374
Solution
−27(5y3+162)
Show Solution
Find the roots
y=−533150
Alternative Form
y≈−3.187976
Evaluate
−y2×135y−4374
To find the roots of the expression,set the expression equal to 0
−y2×135y−4374=0
Multiply
More Steps
Multiply the terms
y2×135y
Multiply the terms with the same base by adding their exponents
y2+1×135
Add the numbers
y3×135
Use the commutative property to reorder the terms
135y3
−135y3−4374=0
Move the constant to the right-hand side and change its sign
−135y3=0+4374
Removing 0 doesn't change the value,so remove it from the expression
−135y3=4374
Change the signs on both sides of the equation
135y3=−4374
Divide both sides
135135y3=135−4374
Divide the numbers
y3=135−4374
Divide the numbers
More Steps
Evaluate
135−4374
Cancel out the common factor 27
5−162
Use b−a=−ba=−ba to rewrite the fraction
−5162
y3=−5162
Take the 3-th root on both sides of the equation
3y3=3−5162
Calculate
y=3−5162
Solution
More Steps
Evaluate
3−5162
An odd root of a negative radicand is always a negative
−35162
To take a root of a fraction,take the root of the numerator and denominator separately
−353162
Simplify the radical expression
More Steps
Evaluate
3162
Write the expression as a product where the root of one of the factors can be evaluated
327×6
Write the number in exponential form with the base of 3
333×6
The root of a product is equal to the product of the roots of each factor
333×36
Reduce the index of the radical and exponent with 3
336
−35336
Multiply by the Conjugate
35×352−336×352
Simplify
35×352−336×325
Multiply the numbers
More Steps
Evaluate
36×325
The product of roots with the same index is equal to the root of the product
36×25
Calculate the product
3150
35×352−33150
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
5−33150
Calculate
−533150
y=−533150
Alternative Form
y≈−3.187976
Show Solution