Solve -6m^2 -9m^24m^5m 8m

Question

Simplify the expression

- 6 m^{2} - 288 m^{9}

Evaluate

- 6 m^{2} - 9 m^{2} \times 4 m^{5} \times m \times 8 m

Solution

More Steps

Evaluate

9 m^{2} \times 4 m^{5} \times m \times 8 m

Multiply the terms

More Steps

Evaluate

9 \times 4 \times 8

Multiply the terms

36 \times 8

Multiply the numbers

288

288 m^{2} \times m^{5} \times m \times m

Multiply the terms with the same base by adding their exponents

288 m^{2 + 5 + 1 + 1}

Add the numbers

288 m^{9}

- 6 m^{2} - 288 m^{9}

Show Solution

Factor the expression

- 6 m^{2} (1 + 48 m^{7})

Evaluate

- 6 m^{2} - 9 m^{2} \times 4 m^{5} \times m \times 8 m

Multiply

More Steps

Evaluate

9 m^{2} \times 4 m^{5} \times m \times 8 m

Multiply the terms

More Steps

Evaluate

9 \times 4 \times 8

Multiply the terms

36 \times 8

Multiply the numbers

288

288 m^{2} \times m^{5} \times m \times m

Multiply the terms with the same base by adding their exponents

288 m^{2 + 5 + 1 + 1}

Add the numbers

288 m^{9}

- 6 m^{2} - 288 m^{9}

Rewrite the expression

- 6 m^{2} - 6 m^{2} \times 48 m^{7}

Solution

- 6 m^{2} (1 + 48 m^{7})

Show Solution

Find the roots

m_{1} = - \frac{7 4 8 ^{6}}{48}, m_{2} = 0

Alternative Form

m_{1} \approx - 0.575205, m_{2} = 0

Evaluate

- 6 m^{2} - 9 m^{2} \times 4 m^{5} \times m \times 8 m

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

- 6 m^{2} - 9 m^{2} \times 4 m^{5} \times m \times 8 m = 0

Multiply

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Multiply the terms

9 m^{2} \times 4 m^{5} \times m \times 8 m

Multiply the terms

More Steps

Evaluate

9 \times 4 \times 8

Multiply the terms

36 \times 8

Multiply the numbers

288

288 m^{2} \times m^{5} \times m \times m

Multiply the terms with the same base by adding their exponents

288 m^{2 + 5 + 1 + 1}

Add the numbers

288 m^{9}

- 6 m^{2} - 288 m^{9} = 0

Factor the expression

- 6 m^{2} (1 + 48 m^{7}) = 0

Divide both sides

m^{2} (1 + 48 m^{7}) = 0

Separate the equation into 2 possible cases

m^{2} = 0 1 + 48 m^{7} = 0

The only way a power can be 0 is when the base equals 0

m = 0 1 + 48 m^{7} = 0

Solve the equation

More Steps

Evaluate

1 + 48 m^{7} = 0

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

48 m^{7} = 0 - 1

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

48 m^{7} = - 1

Divide both sides

\frac{48 m ^{7}}{48} = \frac{- 1}{48}

Divide the numbers

m^{7} = \frac{- 1}{48}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

m^{7} = - \frac{1}{48}

Take the 7 -th root on both sides of the equation

7 m^{7} = 7 - \frac{1}{48}

Calculate

m = 7 - \frac{1}{48}

Simplify the root

More Steps

Evaluate

7 - \frac{1}{48}

An odd root of a negative radicand is always a negative

- 7 \frac{1}{48}

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

- \frac{7 1}{7 48}

Simplify the radical expression

- \frac{1}{7 48}

Multiply by the Conjugate

\frac{- 7 4 8 ^{6}}{7 48 \times 7 4 8 ^{6}}

Multiply the numbers

\frac{- 7 4 8 ^{6}}{48}

Calculate

- \frac{7 4 8 ^{6}}{48}

m = - \frac{7 4 8 ^{6}}{48}

m = 0 m = - \frac{7 4 8 ^{6}}{48}

Solution

m_{1} = - \frac{7 4 8 ^{6}}{48}, m_{2} = 0

Alternative Form

m_{1} \approx - 0.575205, m_{2} = 0

Show Solution