Solve M^55629/4-101

Question

Simplify the expression

\frac{5629}{4} M^{5} - 101

Evaluate

M^{5} \times \frac{5629}{4} - 101

Solution

\frac{5629}{4} M^{5} - 101

Show Solution

\frac{1}{4} (5629 M^{5} - 404)

Evaluate

M^{5} \times \frac{5629}{4} - 101

Use the commutative property to reorder the terms

\frac{5629}{4} M^{5} - 101

Solution

\frac{1}{4} (5629 M^{5} - 404)

Show Solution

M = \frac{5 404 \times 562 9 ^{4}}{5629}

Alternative Form

M \approx 0.590459

Evaluate

M^{5} \times \frac{5629}{4} - 101

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

M^{5} \times \frac{5629}{4} - 101 = 0

Use the commutative property to reorder the terms

\frac{5629}{4} M^{5} - 101 = 0

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

\frac{5629}{4} M^{5} = 0 + 101

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

\frac{5629}{4} M^{5} = 101

Multiply by the reciprocal

\frac{5629}{4} M^{5} \times \frac{4}{5629} = 101 \times \frac{4}{5629}

Multiply

M^{5} = 101 \times \frac{4}{5629}

Multiply

More Steps

Evaluate

101 \times \frac{4}{5629}

Multiply the numbers

\frac{101 \times 4}{5629}

Multiply the numbers

\frac{404}{5629}

M^{5} = \frac{404}{5629}

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

5 M^{5} = 5 \frac{404}{5629}

Calculate

M = 5 \frac{404}{5629}

Solution

More Steps

Evaluate

5 \frac{404}{5629}

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

\frac{5 404}{5 5629}

Multiply by the Conjugate

\frac{5 404 \times 5 562 9 ^{4}}{5 5629 \times 5 562 9 ^{4}}

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

\frac{5 404 \times 562 9 ^{4}}{5 5629 \times 5 562 9 ^{4}}

Multiply the numbers

More Steps

Evaluate

55629 \times 5 562 9^{4}

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

5 5629 \times 562 9^{4}

Calculate the product

5 562 9^{5}

Reduce the index of the radical and exponent with 5

5629

\frac{5 404 \times 562 9 ^{4}}{5629}

M = \frac{5 404 \times 562 9 ^{4}}{5629}

Alternative Form

M \approx 0.590459

Show Solution