Solve 5(n n^4)=22 (8(n^2 n^6)) - Socratic AI (ScanMath)

Question

Solve the equation

n_{1} = 0, n_{2} = \frac{3 2420}{44}

Alternative Form

n_{1} = 0, n_{2} \approx 0.305131

Evaluate

5 (n \times n^{4}) = 22 (8 (n^{2} \times n^{6}))

Remove the parentheses

5 n \times n^{4} = 22 \times 8 n^{2} \times n^{6}

Multiply

More Steps

Evaluate

5 n \times n^{4}

Multiply the terms with the same base by adding their exponents

5 n^{1 + 4}

Add the numbers

5 n^{5}

5 n^{5} = 22 \times 8 n^{2} \times n^{6}

Multiply

More Steps

Evaluate

22 \times 8 n^{2} \times n^{6}

Multiply the terms

176 n^{2} \times n^{6}

Multiply the terms with the same base by adding their exponents

176 n^{2 + 6}

Add the numbers

176 n^{8}

5 n^{5} = 176 n^{8}

Add or subtract both sides

5 n^{5} - 176 n^{8} = 0

Factor the expression

n^{5} (5 - 176 n^{3}) = 0

Separate the equation into 2 possible cases

n^{5} = 0 5 - 176 n^{3} = 0

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

n = 0 5 - 176 n^{3} = 0

Solve the equation

More Steps

Evaluate

5 - 176 n^{3} = 0

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

- 176 n^{3} = 0 - 5

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

- 176 n^{3} = - 5

Change the signs on both sides of the equation

176 n^{3} = 5

Divide both sides

\frac{176 n ^{3}}{176} = \frac{5}{176}

Divide the numbers

n^{3} = \frac{5}{176}

Take the 3 -th root on both sides of the equation

3 n^{3} = 3 \frac{5}{176}

Calculate

n = 3 \frac{5}{176}

Simplify the root

More Steps

Evaluate

3 \frac{5}{176}

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

\frac{3 5}{3 176}

Simplify the radical expression

\frac{3 5}{2 3 22}

Multiply by the Conjugate

\frac{3 5 \times 3 2 2 ^{2}}{2 3 22 \times 3 2 2 ^{2}}

Simplify

\frac{3 5 \times 3 484}{2 3 22 \times 3 2 2 ^{2}}

Multiply the numbers

\frac{3 2420}{2 3 22 \times 3 2 2 ^{2}}

Multiply the numbers

\frac{3 2420}{44}

n = \frac{3 2420}{44}

n = 0 n = \frac{3 2420}{44}

Solution

n_{1} = 0, n_{2} = \frac{3 2420}{44}

Alternative Form

n_{1} = 0, n_{2} \approx 0.305131

Show Solution