Solve m^66-2960-1

Question

Simplify the expression

6 m^{6} - 2961

Evaluate

m^{6} \times 6 - 2960 - 1

Use the commutative property to reorder the terms

6 m^{6} - 2960 - 1

Solution

6 m^{6} - 2961

Show Solution

3 (2 m^{6} - 987)

Evaluate

m^{6} \times 6 - 2960 - 1

Use the commutative property to reorder the terms

6 m^{6} - 2960 - 1

Subtract the numbers

6 m^{6} - 2961

Solution

3 (2 m^{6} - 987)

Show Solution

m_{1} = - \frac{6 31584}{2}, m_{2} = \frac{6 31584}{2}

Alternative Form

m_{1} \approx - 2.811132, m_{2} \approx 2.811132

Evaluate

m^{6} \times 6 - 2960 - 1

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

m^{6} \times 6 - 2960 - 1 = 0

Use the commutative property to reorder the terms

6 m^{6} - 2960 - 1 = 0

Subtract the numbers

6 m^{6} - 2961 = 0

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

6 m^{6} = 0 + 2961

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

6 m^{6} = 2961

Divide both sides

\frac{6 m ^{6}}{6} = \frac{2961}{6}

Divide the numbers

m^{6} = \frac{2961}{6}

Cancel out the common factor 3

m^{6} = \frac{987}{2}

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

m = \pm 6 \frac{987}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{987}{2}

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

\frac{6 987}{6 2}

Multiply by the Conjugate

\frac{6 987 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 987 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

6987 \times 632

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

6 987 \times 32

Calculate the product

631584

\frac{6 31584}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 6 2^{5}

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

6 2 \times 2^{5}

Calculate the product

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 31584}{2}

m = \pm \frac{6 31584}{2}

Separate the equation into 2 possible cases

m = \frac{6 31584}{2} m = - \frac{6 31584}{2}

Solution

m_{1} = - \frac{6 31584}{2}, m_{2} = \frac{6 31584}{2}

Alternative Form

m_{1} \approx - 2.811132, m_{2} \approx 2.811132

Show Solution