Solve 16-3y^4y=27

Question

Solve the equation

y = - \frac{5 891}{3}

Alternative Form

y \approx - 1.296744

Evaluate

16 - 3 y^{4} \times y = 27

Multiply

More Steps

Evaluate

3 y^{4} \times y

Multiply the terms with the same base by adding their exponents

3 y^{4 + 1}

Add the numbers

3 y^{5}

16 - 3 y^{5} = 27

Move the constant to the right-hand side and change its sign

- 3 y^{5} = 27 - 16

Subtract the numbers

- 3 y^{5} = 11

Change the signs on both sides of the equation

3 y^{5} = - 11

Divide both sides

\frac{3 y ^{5}}{3} = \frac{- 11}{3}

Divide the numbers

y^{5} = \frac{- 11}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{5} = - \frac{11}{3}

Take the 5 -th root on both sides of the equation

5 y^{5} = 5 - \frac{11}{3}

Calculate

y = 5 - \frac{11}{3}

Solution

More Steps

Evaluate

5 - \frac{11}{3}

An odd root of a negative radicand is always a negative

- 5 \frac{11}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{5 11}{5 3}

Rewrite the expression

\frac{- 5 11}{5 3}

Multiply by the Conjugate

\frac{- 5 11 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{- 5 11 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

- 511 \times 581

The product of roots with the same index is equal to the root of the product

- 5 11 \times 81

Calculate the product

- 5891

\frac{- 5 891}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

The product of roots with the same index is equal to the root of the product

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{- 5 891}{3}

Calculate

- \frac{5 891}{3}

y = - \frac{5 891}{3}

Alternative Form

y \approx - 1.296744

Show Solution