Solve 7y^4y^2728=90

Question

Solve the equation

y_{1} = - \frac{6 45 \times 254 8 ^{5}}{2548}, y_{2} = \frac{6 45 \times 254 8 ^{5}}{2548}

Alternative Form

y_{1} \approx - 0.510312, y_{2} \approx 0.510312

Evaluate

7 y^{4} \times y^{2} \times 728 = 90

Multiply

More Steps

Evaluate

7 y^{4} \times y^{2} \times 728

Multiply the terms

5096 y^{4} \times y^{2}

Multiply the terms with the same base by adding their exponents

5096 y^{4 + 2}

Add the numbers

5096 y^{6}

5096 y^{6} = 90

Divide both sides

\frac{5096 y ^{6}}{5096} = \frac{90}{5096}

Divide the numbers

y^{6} = \frac{90}{5096}

Cancel out the common factor 2

y^{6} = \frac{45}{2548}

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

y = \pm 6 \frac{45}{2548}

Simplify the expression

More Steps

Evaluate

6 \frac{45}{2548}

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

\frac{6 45}{6 2548}

Multiply by the Conjugate

\frac{6 45 \times 6 254 8 ^{5}}{6 2548 \times 6 254 8 ^{5}}

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

\frac{6 45 \times 254 8 ^{5}}{6 2548 \times 6 254 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

62548 \times 6 254 8^{5}

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

6 2548 \times 254 8^{5}

Calculate the product

6 254 8^{6}

Reduce the index of the radical and exponent with 6

2548

\frac{6 45 \times 254 8 ^{5}}{2548}

y = \pm \frac{6 45 \times 254 8 ^{5}}{2548}

Separate the equation into 2 possible cases

y = \frac{6 45 \times 254 8 ^{5}}{2548} y = - \frac{6 45 \times 254 8 ^{5}}{2548}

Solution

y_{1} = - \frac{6 45 \times 254 8 ^{5}}{2548}, y_{2} = \frac{6 45 \times 254 8 ^{5}}{2548}

Alternative Form

y_{1} \approx - 0.510312, y_{2} \approx 0.510312

Show Solution