Solve a^2/5 = a^5/8

Evaluate

\frac{a ^{2}}{5} = \frac{a ^{5}}{8}

Cross multiply

a^{2} \times 8 = 5 a^{5}

Simplify the equation

8 a^{2} = 5 a^{5}

Add or subtract both sides

8 a^{2} - 5 a^{5} = 0

Factor the expression

a^{2} (8 - 5 a^{3}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 8 - 5 a^{3} = 0

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

a = 0 8 - 5 a^{3} = 0

Solve the equation

More Steps

a = 0 a = \frac{2 3 25}{5}

Solution

a_{1} = 0, a_{2} = \frac{2 3 25}{5}

Alternative Form

a_{1} = 0, a_{2} \approx 1.169607

Solve the equation