Solve 46m^34m 11m-15m-17m

Question

Simplify the expression

2024 m^{5} - 32 m

Evaluate

46 m^{3} \times 4 m \times 11 m - 15 m - 17 m

Multiply

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Multiply the terms

46 m^{3} \times 4 m \times 11 m

Multiply the terms

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Evaluate

46 \times 4 \times 11

Multiply the terms

184 \times 11

Multiply the numbers

2024

2024 m^{3} \times m \times m

Multiply the terms with the same base by adding their exponents

2024 m^{3 + 1 + 1}

Add the numbers

2024 m^{5}

2024 m^{5} - 15 m - 17 m

Solution

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Evaluate

- 15 m - 17 m

Collect like terms by calculating the sum or difference of their coefficients

(- 15 - 17) m

Subtract the numbers

- 32 m

2024 m^{5} - 32 m

Show Solution

Factor the expression

8 m (253 m^{4} - 4)

Evaluate

46 m^{3} \times 4 m \times 11 m - 15 m - 17 m

Multiply

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Multiply the terms

46 m^{3} \times 4 m \times 11 m

Multiply the terms

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Evaluate

46 \times 4 \times 11

Multiply the terms

184 \times 11

Multiply the numbers

2024

2024 m^{3} \times m \times m

Multiply the terms with the same base by adding their exponents

2024 m^{3 + 1 + 1}

Add the numbers

2024 m^{5}

2024 m^{5} - 15 m - 17 m

Subtract the terms

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Evaluate

- 15 m - 17 m

Collect like terms by calculating the sum or difference of their coefficients

(- 15 - 17) m

Subtract the numbers

- 32 m

2024 m^{5} - 32 m

Rewrite the expression

8 m \times 253 m^{4} - 8 m \times 4

Solution

8 m (253 m^{4} - 4)

Show Solution

Find the roots

m_{1} = - \frac{4 4 \times 25 3 ^{3}}{253}, m_{2} = 0, m_{3} = \frac{4 4 \times 25 3 ^{3}}{253}

Alternative Form

m_{1} \approx - 0.354597, m_{2} = 0, m_{3} \approx 0.354597

Evaluate

46 m^{3} \times 4 m \times 11 m - 15 m - 17 m

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

46 m^{3} \times 4 m \times 11 m - 15 m - 17 m = 0

Multiply

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Multiply the terms

46 m^{3} \times 4 m \times 11 m

Multiply the terms

More Steps

Evaluate

46 \times 4 \times 11

Multiply the terms

184 \times 11

Multiply the numbers

2024

2024 m^{3} \times m \times m

Multiply the terms with the same base by adding their exponents

2024 m^{3 + 1 + 1}

Add the numbers

2024 m^{5}

2024 m^{5} - 15 m - 17 m = 0

Subtract the terms

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Simplify

2024 m^{5} - 15 m - 17 m

Subtract the terms

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Evaluate

- 15 m - 17 m

Collect like terms by calculating the sum or difference of their coefficients

(- 15 - 17) m

Subtract the numbers

- 32 m

2024 m^{5} - 32 m

2024 m^{5} - 32 m = 0

Factor the expression

8 m (253 m^{4} - 4) = 0

Divide both sides

m (253 m^{4} - 4) = 0

Separate the equation into 2 possible cases

m = 0 253 m^{4} - 4 = 0

Solve the equation

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Evaluate

253 m^{4} - 4 = 0

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

253 m^{4} = 0 + 4

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

253 m^{4} = 4

Divide both sides

\frac{253 m ^{4}}{253} = \frac{4}{253}

Divide the numbers

m^{4} = \frac{4}{253}

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

m = \pm 4 \frac{4}{253}

Simplify the expression

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Evaluate

4 \frac{4}{253}

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

\frac{4 4}{4 253}

Simplify the radical expression

\frac{2}{4 253}

Multiply by the Conjugate

\frac{2 \times 4 25 3 ^{3}}{4 253 \times 4 25 3 ^{3}}

Multiply the numbers

\frac{4 4 \times 25 3 ^{3}}{4 253 \times 4 25 3 ^{3}}

Multiply the numbers

\frac{4 4 \times 25 3 ^{3}}{253}

m = \pm \frac{4 4 \times 25 3 ^{3}}{253}

Separate the equation into 2 possible cases

m = \frac{4 4 \times 25 3 ^{3}}{253} m = - \frac{4 4 \times 25 3 ^{3}}{253}

m = 0 m = \frac{4 4 \times 25 3 ^{3}}{253} m = - \frac{4 4 \times 25 3 ^{3}}{253}

Solution

m_{1} = - \frac{4 4 \times 25 3 ^{3}}{253}, m_{2} = 0, m_{3} = \frac{4 4 \times 25 3 ^{3}}{253}

Alternative Form

m_{1} \approx - 0.354597, m_{2} = 0, m_{3} \approx 0.354597

Show Solution