Solve 1/3^6x^3=1/3^3x^4

Evaluate

\frac{1}{3 ^{6}} \times x^{3} = \frac{1}{3 ^{3}} \times x^{4}

Rewrite the expression

\frac{x ^{3}}{3 ^{6}} = \frac{x ^{4}}{3 ^{3}}

Cross multiply

x^{3} \times 3^{3} = 3^{6} x^{4}

Simplify the equation

3^{3} x^{3} = 3^{6} x^{4}

Rewrite the expression

3^{3} x^{3} = 3^{3} \times 27 x^{4}

Evaluate

x^{3} = 27 x^{4}

Move the expression to the left side

x^{3} - 27 x^{4} = 0

Factor the expression

x^{3} (1 - 27 x) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 27 x = 0

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

x = 0 1 - 27 x = 0

Solve the equation

More Steps

x = 0 x = \frac{1}{27}

Solution

x_{1} = 0, x_{2} = \frac{1}{27}

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{0} 3 \dot{7}

Solve the equation