Solve 11=32 (4x^6)

Question

Solve the equation

x_{1} = - \frac{6 352}{4}, x_{2} = \frac{6 352}{4}

Alternative Form

x_{1} \approx - 0.664299, x_{2} \approx 0.664299

Evaluate

11 = 32 \times 4 x^{6}

Multiply the numbers

11 = 128 x^{6}

Swap the sides of the equation

128 x^{6} = 11

Divide both sides

\frac{128 x ^{6}}{128} = \frac{11}{128}

Divide the numbers

x^{6} = \frac{11}{128}

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

x = \pm 6 \frac{11}{128}

Simplify the expression

More Steps

Evaluate

6 \frac{11}{128}

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

\frac{6 11}{6 128}

Simplify the radical expression

More Steps

Evaluate

6128

Write the expression as a product where the root of one of the factors can be evaluated

6 64 \times 2

Write the number in exponential form with the base of 2

6 2^{6} \times 2

The root of a product is equal to the product of the roots of each factor

6 2^{6} \times 62

Reduce the index of the radical and exponent with 6

262

\frac{6 11}{2 6 2}

Multiply by the Conjugate

\frac{6 11 \times 6 2 ^{5}}{2 6 2 \times 6 2 ^{5}}

Simplify

\frac{6 11 \times 6 32}{2 6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

611 \times 632

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

6 11 \times 32

Calculate the product

6352

\frac{6 352}{2 6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

262 \times 6 2^{5}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{6 352}{4}

x = \pm \frac{6 352}{4}

Separate the equation into 2 possible cases

x = \frac{6 352}{4} x = - \frac{6 352}{4}

Solution

x_{1} = - \frac{6 352}{4}, x_{2} = \frac{6 352}{4}

Alternative Form

x_{1} \approx - 0.664299, x_{2} \approx 0.664299

Show Solution