Solve a1-a^2 a^3 a^2n=0

Question

Solve the equation

Solve for a

Solve for n

a = 0 a = \frac{6 n ^{5}}{∣ n ∣} a = - \frac{6 n ^{5}}{∣ n ∣}

Evaluate

a \times 1 - a^{2} \times a^{3} \times a^{2} n = 0

Simplify

More Steps

Evaluate

a \times 1 - a^{2} \times a^{3} \times a^{2} n

Any expression multiplied by 1 remains the same

a - a^{2} \times a^{3} \times a^{2} n

Multiply

More Steps

Multiply the terms

a^{2} \times a^{3} \times a^{2} n

Multiply the terms with the same base by adding their exponents

a^{2 + 3 + 2} n

Add the numbers

a^{7} n

a - a^{7} n

a - a^{7} n = 0

Rewrite the expression

a - n a^{7} = 0

Factor the expression

a (1 - n a^{6}) = 0

Separate the equation into 2 possible cases

a = 0 1 - n a^{6} = 0

Solution

More Steps

Evaluate

1 - n a^{6} = 0

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

- n a^{6} = 0 - 1

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

- n a^{6} = - 1

Divide both sides

\frac{- n a ^{6}}{- n} = \frac{- 1}{- n}

Divide the numbers

a^{6} = \frac{- 1}{- n}

Divide the numbers

a^{6} = \frac{1}{n}

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

a = \pm 6 \frac{1}{n}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{n}

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

\frac{6 1}{6 n}

Simplify the radical expression

\frac{1}{6 n}

Multiply by the Conjugate

\frac{1 \times 6 n ^{5}}{6 n \times 6 n ^{5}}

Calculate

\frac{1 \times 6 n ^{5}}{∣ n ∣}

Calculate

\frac{6 n ^{5}}{∣ n ∣}

a = \pm \frac{6 n ^{5}}{∣ n ∣}

Separate the equation into 2 possible cases

a = \frac{6 n ^{5}}{∣ n ∣} a = - \frac{6 n ^{5}}{∣ n ∣}

a = 0 a = \frac{6 n ^{5}}{∣ n ∣} a = - \frac{6 n ^{5}}{∣ n ∣}

Show Solution