Solve 55/x^6=6 - ScanMath

Question

Solve the equation

x_{1} = - \frac{6 427680}{6}, x_{2} = \frac{6 427680}{6}

Alternative Form

x_{1} \approx - 1.446667, x_{2} \approx 1.446667

Evaluate

\frac{55}{x ^{6}} = 6

Find the domain

More Steps

Evaluate

x^{6} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

\frac{55}{x ^{6}} = 6, x \neq = 0

Cross multiply

55 = x^{6} \times 6

Simplify the equation

55 = 6 x^{6}

Swap the sides of the equation

6 x^{6} = 55

Divide both sides

\frac{6 x ^{6}}{6} = \frac{55}{6}

Divide the numbers

x^{6} = \frac{55}{6}

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

x = \pm 6 \frac{55}{6}

Simplify the expression

More Steps

Evaluate

6 \frac{55}{6}

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

\frac{6 55}{6 6}

Multiply by the Conjugate

\frac{6 55 \times 6 6 ^{5}}{6 6 \times 6 6 ^{5}}

Simplify

\frac{6 55 \times 6 7776}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

655 \times 67776

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

6 55 \times 7776

Calculate the product

6427680

\frac{6 427680}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

66 \times 6 6^{5}

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

6 6 \times 6^{5}

Calculate the product

6 6^{6}

Reduce the index of the radical and exponent with 6

6

\frac{6 427680}{6}

x = \pm \frac{6 427680}{6}

Separate the equation into 2 possible cases

x = \frac{6 427680}{6} x = - \frac{6 427680}{6}

Check if the solution is in the defined range

x = \frac{6 427680}{6} x = - \frac{6 427680}{6}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{6 427680}{6} x = - \frac{6 427680}{6}

Solution

x_{1} = - \frac{6 427680}{6}, x_{2} = \frac{6 427680}{6}

Alternative Form

x_{1} \approx - 1.446667, x_{2} \approx 1.446667

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