Solve 7y^4y^27=28

Question

Solve the equation

y_{1} = - \frac{6 67228}{7}, y_{2} = \frac{6 67228}{7}

Alternative Form

y_{1} \approx - 0.910948, y_{2} \approx 0.910948

Evaluate

7 y^{4} \times y^{2} \times 7 = 28

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

49 y^{4 + 2}

Add the numbers

49 y^{6}

49 y^{6} = 28

Divide both sides

\frac{49 y ^{6}}{49} = \frac{28}{49}

Divide the numbers

y^{6} = \frac{28}{49}

Cancel out the common factor 7

y^{6} = \frac{4}{7}

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

y = \pm 6 \frac{4}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{4}{7}

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

\frac{6 4}{6 7}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{3 2}{6 7}

Multiply by the Conjugate

\frac{3 2 \times 6 7 ^{5}}{6 7 \times 6 7 ^{5}}

Simplify

\frac{3 2 \times 6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

32 \times 616807

Use n a = mn a^{m} to expand the expression

6 2^{2} \times 616807

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

6 2^{2} \times 16807

Calculate the product

667228

\frac{6 67228}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

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

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 67228}{7}

y = \pm \frac{6 67228}{7}

Separate the equation into 2 possible cases

y = \frac{6 67228}{7} y = - \frac{6 67228}{7}

Solution

y_{1} = - \frac{6 67228}{7}, y_{2} = \frac{6 67228}{7}

Alternative Form

y_{1} \approx - 0.910948, y_{2} \approx 0.910948

Show Solution