Solve -8y^56y^48y^3 -6y^2

Question

Simplify the expression

- 384 y^{12} - 6 y^{2}

Evaluate

- 8 y^{5} \times 6 y^{4} \times 8 y^{3} - 6 y^{2}

Solution

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Evaluate

- 8 y^{5} \times 6 y^{4} \times 8 y^{3}

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

- 384 y^{5} \times y^{4} \times y^{3}

Multiply the terms with the same base by adding their exponents

- 384 y^{5 + 4 + 3}

Add the numbers

- 384 y^{12}

- 384 y^{12} - 6 y^{2}

Show Solution

Factor the expression

- 6 y^{2} (64 y^{10} + 1)

Evaluate

- 8 y^{5} \times 6 y^{4} \times 8 y^{3} - 6 y^{2}

Multiply

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Evaluate

- 8 y^{5} \times 6 y^{4} \times 8 y^{3}

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

- 384 y^{5} \times y^{4} \times y^{3}

Multiply the terms with the same base by adding their exponents

- 384 y^{5 + 4 + 3}

Add the numbers

- 384 y^{12}

- 384 y^{12} - 6 y^{2}

Rewrite the expression

- 6 y^{2} \times 64 y^{10} - 6 y^{2}

Solution

- 6 y^{2} (64 y^{10} + 1)

Show Solution

Find the roots

y_{1} \approx - 0.627463 + 0.203875 i, y_{2} \approx 0.627463 - 0.203875 i, y_{3} = 0

Evaluate

- 8 y^{5} \times 6 y^{4} \times 8 y^{3} - 6 y^{2}

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

- 8 y^{5} \times 6 y^{4} \times 8 y^{3} - 6 y^{2} = 0

Multiply

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Multiply the terms

- 8 y^{5} \times 6 y^{4} \times 8 y^{3}

Multiply the terms

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Evaluate

8 \times 6 \times 8

Multiply the terms

48 \times 8

Multiply the numbers

384

- 384 y^{5} \times y^{4} \times y^{3}

Multiply the terms with the same base by adding their exponents

- 384 y^{5 + 4 + 3}

Add the numbers

- 384 y^{12}

- 384 y^{12} - 6 y^{2} = 0

Factor the expression

- 6 y^{2} (64 y^{10} + 1) = 0

Divide both sides

y^{2} (64 y^{10} + 1) = 0

Separate the equation into 2 possible cases

y^{2} = 0 64 y^{10} + 1 = 0

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

y = 0 64 y^{10} + 1 = 0

Solve the equation

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Evaluate

64 y^{10} + 1 = 0

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

64 y^{10} = 0 - 1

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

64 y^{10} = - 1

Divide both sides

\frac{64 y ^{10}}{64} = \frac{- 1}{64}

Divide the numbers

y^{10} = \frac{- 1}{64}

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

y^{10} = - \frac{1}{64}

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

y = \pm 10 - \frac{1}{64}

Simplify the expression

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Evaluate

10 - \frac{1}{64}

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

\frac{10 1}{10 - 64}

Simplify the radical expression

\frac{1}{10 - 64}

Simplify the radical expression

\frac{1}{1.441532 + 0.468382 i}

Multiply by the Conjugate

\frac{1.441532 - 0.468382 i}{( 1.441532 + 0.468382 i ) ( 1.441532 - 0.468382 i )}

Calculate

\frac{1.441532 - 0.468382 i}{2.297397}

Divide the terms

0.627463 - 0.203875 i

y = \pm (0.627463 - 0.203875 i)

Separate the equation into 2 possible cases

y \approx 0.627463 - 0.203875 i y \approx - 0.627463 + 0.203875 i

y = 0 y \approx 0.627463 - 0.203875 i y \approx - 0.627463 + 0.203875 i

Solution

y_{1} \approx - 0.627463 + 0.203875 i, y_{2} \approx 0.627463 - 0.203875 i, y_{3} = 0

Show Solution