Solve 15/9 y^4/6 = 9

Question

Solve the equation

y_{1} = - \frac{3 4 250}{5}, y_{2} = \frac{3 4 250}{5}

Alternative Form

y_{1} \approx - 2.385812, y_{2} \approx 2.385812

Evaluate

\frac{15}{9} \times \frac{y ^{4}}{6} = 9

Simplify

More Steps

Evaluate

\frac{15}{9} \times \frac{y ^{4}}{6}

Cancel out the common factor 3

\frac{5}{3} \times \frac{y ^{4}}{6}

Multiply the terms

\frac{5 y ^{4}}{3 \times 6}

Multiply the terms

\frac{5 y ^{4}}{18}

\frac{5 y ^{4}}{18} = 9

Cross multiply

5 y^{4} = 18 \times 9

Simplify the equation

5 y^{4} = 162

Divide both sides

\frac{5 y ^{4}}{5} = \frac{162}{5}

Divide the numbers

y^{4} = \frac{162}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm 4 \frac{162}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{162}{5}

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

\frac{4 162}{4 5}

Simplify the radical expression

More Steps

Evaluate

4162

Write the expression as a product where the root of one of the factors can be evaluated

4 81 \times 2

Write the number in exponential form with the base of 3

4 3^{4} \times 2

The root of a product is equal to the product of the roots of each factor

4 3^{4} \times 42

Reduce the index of the radical and exponent with 4

342

\frac{3 4 2}{4 5}

Multiply by the Conjugate

\frac{3 4 2 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{3 4 2 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4125

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

4 2 \times 125

Calculate the product

4250

\frac{3 4 250}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{3 4 250}{5}

y = \pm \frac{3 4 250}{5}

Separate the equation into 2 possible cases

y = \frac{3 4 250}{5} y = - \frac{3 4 250}{5}

Solution

y_{1} = - \frac{3 4 250}{5}, y_{2} = \frac{3 4 250}{5}

Alternative Form

y_{1} \approx - 2.385812, y_{2} \approx 2.385812

Show Solution