Solve 4y^5y=117 - ScanMath

Question

Solve the equation

y_{1} = - \frac{6 1872}{2}, y_{2} = \frac{6 1872}{2}

Alternative Form

y_{1} \approx - 1.755312, y_{2} \approx 1.755312

Evaluate

4 y^{5} \times y = 117

Multiply

More Steps

Evaluate

4 y^{5} \times y

Multiply the terms with the same base by adding their exponents

4 y^{5 + 1}

Add the numbers

4 y^{6}

4 y^{6} = 117

Divide both sides

\frac{4 y ^{6}}{4} = \frac{117}{4}

Divide the numbers

y^{6} = \frac{117}{4}

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

y = \pm 6 \frac{117}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{117}{4}

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

\frac{6 117}{6 4}

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{6 117}{3 2}

Multiply by the Conjugate

\frac{6 117 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{6 117 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

6117 \times 34

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

6117 \times 6 4^{2}

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

6 117 \times 4^{2}

Calculate the product

61872

\frac{6 1872}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{6 1872}{2}

y = \pm \frac{6 1872}{2}

Separate the equation into 2 possible cases

y = \frac{6 1872}{2} y = - \frac{6 1872}{2}

Solution

y_{1} = - \frac{6 1872}{2}, y_{2} = \frac{6 1872}{2}

Alternative Form

y_{1} \approx - 1.755312, y_{2} \approx 1.755312

Show Solution