Solve M^55629/6-390

Question

Simplify the expression

\frac{5629}{6} M^{5} - 390

Evaluate

M^{5} \times \frac{5629}{6} - 390

Solution

\frac{5629}{6} M^{5} - 390

Show Solution

\frac{13}{6} (433 M^{5} - 180)

Evaluate

M^{5} \times \frac{5629}{6} - 390

Use the commutative property to reorder the terms

\frac{5629}{6} M^{5} - 390

Solution

\frac{13}{6} (433 M^{5} - 180)

Show Solution

M = \frac{5 180 \times 43 3 ^{4}}{433}

Alternative Form

M \approx 0.83899

Evaluate

M^{5} \times \frac{5629}{6} - 390

To find the roots of the expression,set the expression equal to 0

M^{5} \times \frac{5629}{6} - 390 = 0

Use the commutative property to reorder the terms

\frac{5629}{6} M^{5} - 390 = 0

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

\frac{5629}{6} M^{5} = 0 + 390

Removing 0 doesn't change the value,so remove it from the expression

\frac{5629}{6} M^{5} = 390

Multiply by the reciprocal

\frac{5629}{6} M^{5} \times \frac{6}{5629} = 390 \times \frac{6}{5629}

Multiply

M^{5} = 390 \times \frac{6}{5629}

Multiply

More Steps

Evaluate

390 \times \frac{6}{5629}

Reduce the numbers

30 \times \frac{6}{433}

Multiply the numbers

\frac{30 \times 6}{433}

Multiply the numbers

\frac{180}{433}

M^{5} = \frac{180}{433}

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

5 M^{5} = 5 \frac{180}{433}

Calculate

M = 5 \frac{180}{433}

Solution

More Steps

Evaluate

5 \frac{180}{433}

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

\frac{5 180}{5 433}

Multiply by the Conjugate

\frac{5 180 \times 5 43 3 ^{4}}{5 433 \times 5 43 3 ^{4}}

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

\frac{5 180 \times 43 3 ^{4}}{5 433 \times 5 43 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

5433 \times 5 43 3^{4}

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

5 433 \times 43 3^{4}

Calculate the product

5 43 3^{5}

Reduce the index of the radical and exponent with 5

433

\frac{5 180 \times 43 3 ^{4}}{433}

M = \frac{5 180 \times 43 3 ^{4}}{433}

Alternative Form

M \approx 0.83899

Show Solution