Question
Simplify the expression
−45u3−16
Evaluate
3u3−6u2×8u−16
Multiply
More Steps

Multiply the terms
−6u2×8u
Multiply the terms
−48u2×u
Multiply the terms with the same base by adding their exponents
−48u2+1
Add the numbers
−48u3
3u3−48u3−16
Solution
More Steps

Evaluate
3u3−48u3
Collect like terms by calculating the sum or difference of their coefficients
(3−48)u3
Subtract the numbers
−45u3
−45u3−16
Show Solution

Find the roots
u=−1523150
Alternative Form
u≈−0.708439
Evaluate
3u3−6u2×8u−16
To find the roots of the expression,set the expression equal to 0
3u3−6u2×8u−16=0
Multiply
More Steps

Multiply the terms
6u2×8u
Multiply the terms
48u2×u
Multiply the terms with the same base by adding their exponents
48u2+1
Add the numbers
48u3
3u3−48u3−16=0
Subtract the terms
More Steps

Simplify
3u3−48u3
Collect like terms by calculating the sum or difference of their coefficients
(3−48)u3
Subtract the numbers
−45u3
−45u3−16=0
Move the constant to the right-hand side and change its sign
−45u3=0+16
Removing 0 doesn't change the value,so remove it from the expression
−45u3=16
Change the signs on both sides of the equation
45u3=−16
Divide both sides
4545u3=45−16
Divide the numbers
u3=45−16
Use b−a=−ba=−ba to rewrite the fraction
u3=−4516
Take the 3-th root on both sides of the equation
3u3=3−4516
Calculate
u=3−4516
Solution
More Steps

Evaluate
3−4516
An odd root of a negative radicand is always a negative
−34516
To take a root of a fraction,take the root of the numerator and denominator separately
−345316
Simplify the radical expression
More Steps

Evaluate
316
Write the expression as a product where the root of one of the factors can be evaluated
38×2
Write the number in exponential form with the base of 2
323×2
The root of a product is equal to the product of the roots of each factor
323×32
Reduce the index of the radical and exponent with 3
232
−345232
Multiply by the Conjugate
345×3452−232×3452
Simplify
345×3452−232×3375
Multiply the numbers
More Steps

Evaluate
−232×3375
Multiply the terms
−632×375
Multiply the terms
−63150
345×3452−63150
Multiply the numbers
More Steps

Evaluate
345×3452
The product of roots with the same index is equal to the root of the product
345×452
Calculate the product
3453
Reduce the index of the radical and exponent with 3
45
45−63150
Cancel out the common factor 3
15−23150
Calculate
−1523150
u=−1523150
Alternative Form
u≈−0.708439
Show Solution
