Solve -4 ⋅ 10-7n^6 = -45

Question

Solve the equation

n_{1} = - \frac{6 84035}{7}, n_{2} = \frac{6 84035}{7}

Alternative Form

n_{1} \approx - 0.945465, n_{2} \approx 0.945465

Evaluate

- 4 \times 10 - 7 n^{6} = - 45

Multiply the numbers

- 40 - 7 n^{6} = - 45

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

- 7 n^{6} = - 45 + 40

Add the numbers

- 7 n^{6} = - 5

Change the signs on both sides of the equation

7 n^{6} = 5

Divide both sides

\frac{7 n ^{6}}{7} = \frac{5}{7}

Divide the numbers

n^{6} = \frac{5}{7}

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

n = \pm 6 \frac{5}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{5}{7}

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

\frac{6 5}{6 7}

Multiply by the Conjugate

\frac{6 5 \times 6 7 ^{5}}{6 7 \times 6 7 ^{5}}

Simplify

\frac{6 5 \times 6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 616807

The product of roots with the same index is equal to the root of the product

6 5 \times 16807

Calculate the product

684035

\frac{6 84035}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

The product of roots with the same index is equal to the root of the product

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 84035}{7}

n = \pm \frac{6 84035}{7}

Separate the equation into 2 possible cases

n = \frac{6 84035}{7} n = - \frac{6 84035}{7}

Solution

n_{1} = - \frac{6 84035}{7}, n_{2} = \frac{6 84035}{7}

Alternative Form

n_{1} \approx - 0.945465, n_{2} \approx 0.945465

Show Solution