Solve a^43a^39a^2=a

Question

Solve the equation

a_{1} = - \frac{8 243}{3}, a_{2} = 0, a_{3} = \frac{8 243}{3}

Alternative Form

a_{1} \approx - 0.662338, a_{2} = 0, a_{3} \approx 0.662338

Evaluate

a^{4} \times 3 a^{3} \times 9 a^{2} = a

Multiply

More Steps

Evaluate

a^{4} \times 3 a^{3} \times 9 a^{2}

Multiply the terms with the same base by adding their exponents

a^{4 + 3 + 2} \times 3 \times 9

Add the numbers

a^{9} \times 3 \times 9

Multiply the terms

a^{9} \times 27

Use the commutative property to reorder the terms

27 a^{9}

27 a^{9} = a

Add or subtract both sides

27 a^{9} - a = 0

Factor the expression

a (27 a^{8} - 1) = 0

Separate the equation into 2 possible cases

a = 0 27 a^{8} - 1 = 0

Solve the equation

More Steps

Evaluate

27 a^{8} - 1 = 0

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

27 a^{8} = 0 + 1

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

27 a^{8} = 1

Divide both sides

\frac{27 a ^{8}}{27} = \frac{1}{27}

Divide the numbers

a^{8} = \frac{1}{27}

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

a = \pm 8 \frac{1}{27}

Simplify the expression

More Steps

Evaluate

8 \frac{1}{27}

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

\frac{8 1}{8 27}

Simplify the radical expression

\frac{1}{8 27}

Multiply by the Conjugate

\frac{8 2 7 ^{7}}{8 27 \times 8 2 7 ^{7}}

Simplify

\frac{3 ^{2} 8 243}{8 27 \times 8 2 7 ^{7}}

Multiply the numbers

\frac{3 ^{2} 8 243}{3 ^{3}}

Reduce the fraction

\frac{8 243}{3}

a = \pm \frac{8 243}{3}

Separate the equation into 2 possible cases

a = \frac{8 243}{3} a = - \frac{8 243}{3}

a = 0 a = \frac{8 243}{3} a = - \frac{8 243}{3}

Solution

a_{1} = - \frac{8 243}{3}, a_{2} = 0, a_{3} = \frac{8 243}{3}

Alternative Form

a_{1} \approx - 0.662338, a_{2} = 0, a_{3} \approx 0.662338

Show Solution