Solve x x^5101=360

Question

Solve the equation

x_{1} = - \frac{6 360 \times 10 1 ^{5}}{101}, x_{2} = \frac{6 360 \times 10 1 ^{5}}{101}

Alternative Form

x_{1} \approx - 1.235938, x_{2} \approx 1.235938

Evaluate

x \times x^{5} \times 101 = 360

Multiply

More Steps

Evaluate

x \times x^{5} \times 101

Multiply the terms with the same base by adding their exponents

x^{1 + 5} \times 101

Add the numbers

x^{6} \times 101

Use the commutative property to reorder the terms

101 x^{6}

101 x^{6} = 360

Divide both sides

\frac{101 x ^{6}}{101} = \frac{360}{101}

Divide the numbers

x^{6} = \frac{360}{101}

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

x = \pm 6 \frac{360}{101}

Simplify the expression

More Steps

Evaluate

6 \frac{360}{101}

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

\frac{6 360}{6 101}

Multiply by the Conjugate

\frac{6 360 \times 6 10 1 ^{5}}{6 101 \times 6 10 1 ^{5}}

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

\frac{6 360 \times 10 1 ^{5}}{6 101 \times 6 10 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

6101 \times 6 10 1^{5}

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

6 101 \times 10 1^{5}

Calculate the product

6 10 1^{6}

Reduce the index of the radical and exponent with 6

101

\frac{6 360 \times 10 1 ^{5}}{101}

x = \pm \frac{6 360 \times 10 1 ^{5}}{101}

Separate the equation into 2 possible cases

x = \frac{6 360 \times 10 1 ^{5}}{101} x = - \frac{6 360 \times 10 1 ^{5}}{101}

Solution

x_{1} = - \frac{6 360 \times 10 1 ^{5}}{101}, x_{2} = \frac{6 360 \times 10 1 ^{5}}{101}

Alternative Form

x_{1} \approx - 1.235938, x_{2} \approx 1.235938

Show Solution