Solve (3s^48s^25s^2)-(4s^25s 1)

Question

Simplify the expression

120 s^{8} - 20 s^{3}

Evaluate

(3 s^{4} \times 8 s^{2} \times 5 s^{2}) - (4 s^{2} \times 5 s \times 1)

Multiply

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Multiply the terms

3 s^{4} \times 8 s^{2} \times 5 s^{2}

Multiply the terms

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Evaluate

3 \times 8 \times 5

Multiply the terms

24 \times 5

Multiply the numbers

120

120 s^{4} \times s^{2} \times s^{2}

Multiply the terms with the same base by adding their exponents

120 s^{4 + 2 + 2}

Add the numbers

120 s^{8}

120 s^{8} - (4 s^{2} \times 5 s \times 1)

Solution

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Multiply the terms

4 s^{2} \times 5 s \times 1

Rewrite the expression

4 s^{2} \times 5 s

Multiply the terms

20 s^{2} \times s

Multiply the terms with the same base by adding their exponents

20 s^{2 + 1}

Add the numbers

20 s^{3}

120 s^{8} - 20 s^{3}

Show Solution

Factor the expression

20 s^{3} (6 s^{5} - 1)

Evaluate

(3 s^{4} \times 8 s^{2} \times 5 s^{2}) - (4 s^{2} \times 5 s \times 1)

Multiply

More Steps

Multiply the terms

3 s^{4} \times 8 s^{2} \times 5 s^{2}

Multiply the terms

More Steps

Evaluate

3 \times 8 \times 5

Multiply the terms

24 \times 5

Multiply the numbers

120

120 s^{4} \times s^{2} \times s^{2}

Multiply the terms with the same base by adding their exponents

120 s^{4 + 2 + 2}

Add the numbers

120 s^{8}

120 s^{8} - (4 s^{2} \times 5 s \times 1)

Multiply the terms

More Steps

Multiply the terms

4 s^{2} \times 5 s \times 1

Rewrite the expression

4 s^{2} \times 5 s

Multiply the terms

20 s^{2} \times s

Multiply the terms with the same base by adding their exponents

20 s^{2 + 1}

Add the numbers

20 s^{3}

120 s^{8} - 20 s^{3}

Rewrite the expression

20 s^{3} \times 6 s^{5} - 20 s^{3}

Solution

20 s^{3} (6 s^{5} - 1)

Show Solution

Find the roots

s_{1} = 0, s_{2} = \frac{5 1296}{6}

Alternative Form

s_{1} = 0, s_{2} \approx 0.698827

Evaluate

(3 s^{4} \times 8 s^{2} \times 5 s^{2}) - (4 s^{2} \times 5 s \times 1)

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

(3 s^{4} \times 8 s^{2} \times 5 s^{2}) - (4 s^{2} \times 5 s \times 1) = 0

Multiply

More Steps

Multiply the terms

3 s^{4} \times 8 s^{2} \times 5 s^{2}

Multiply the terms

More Steps

Evaluate

3 \times 8 \times 5

Multiply the terms

24 \times 5

Multiply the numbers

120

120 s^{4} \times s^{2} \times s^{2}

Multiply the terms with the same base by adding their exponents

120 s^{4 + 2 + 2}

Add the numbers

120 s^{8}

120 s^{8} - (4 s^{2} \times 5 s \times 1) = 0

Multiply the terms

More Steps

Multiply the terms

4 s^{2} \times 5 s \times 1

Rewrite the expression

4 s^{2} \times 5 s

Multiply the terms

20 s^{2} \times s

Multiply the terms with the same base by adding their exponents

20 s^{2 + 1}

Add the numbers

20 s^{3}

120 s^{8} - 20 s^{3} = 0

Factor the expression

20 s^{3} (6 s^{5} - 1) = 0

Divide both sides

s^{3} (6 s^{5} - 1) = 0

Separate the equation into 2 possible cases

s^{3} = 0 6 s^{5} - 1 = 0

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

s = 0 6 s^{5} - 1 = 0

Solve the equation

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Evaluate

6 s^{5} - 1 = 0

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

6 s^{5} = 0 + 1

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

6 s^{5} = 1

Divide both sides

\frac{6 s ^{5}}{6} = \frac{1}{6}

Divide the numbers

s^{5} = \frac{1}{6}

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

5 s^{5} = 5 \frac{1}{6}

Calculate

s = 5 \frac{1}{6}

Simplify the root

More Steps

Evaluate

5 \frac{1}{6}

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

\frac{5 1}{5 6}

Simplify the radical expression

\frac{1}{5 6}

Multiply by the Conjugate

\frac{5 6 ^{4}}{5 6 \times 5 6 ^{4}}

Simplify

\frac{5 1296}{5 6 \times 5 6 ^{4}}

Multiply the numbers

\frac{5 1296}{6}

s = \frac{5 1296}{6}

s = 0 s = \frac{5 1296}{6}

Solution

s_{1} = 0, s_{2} = \frac{5 1296}{6}

Alternative Form

s_{1} = 0, s_{2} \approx 0.698827

Show Solution