Solve x^211x^28x^22x-8

Question

Simplify the expression

176 x^{7} - 8

Evaluate

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x - 8

Solution

More Steps

Evaluate

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 2 + 2 + 1} \times 11 \times 8 \times 2

Add the numbers

x^{7} \times 11 \times 8 \times 2

Multiply the terms

More Steps

Evaluate

11 \times 8 \times 2

Multiply the terms

88 \times 2

Multiply the numbers

176

x^{7} \times 176

Use the commutative property to reorder the terms

176 x^{7}

176 x^{7} - 8

Show Solution

Factor the expression

8 (22 x^{7} - 1)

Evaluate

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x - 8

Multiply

More Steps

Evaluate

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 2 + 2 + 1} \times 11 \times 8 \times 2

Add the numbers

x^{7} \times 11 \times 8 \times 2

Multiply the terms

More Steps

Evaluate

11 \times 8 \times 2

Multiply the terms

88 \times 2

Multiply the numbers

176

x^{7} \times 176

Use the commutative property to reorder the terms

176 x^{7}

176 x^{7} - 8

Solution

8 (22 x^{7} - 1)

Show Solution

Find the roots

x = \frac{7 2 2 ^{6}}{22}

Alternative Form

x \approx 0.643021

Evaluate

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x - 8

To find the roots of the expression,set the expression equal to 0

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x - 8 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 11 x^{2} \times 8 x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 2 + 2 + 1} \times 11 \times 8 \times 2

Add the numbers

x^{7} \times 11 \times 8 \times 2

Multiply the terms

More Steps

Evaluate

11 \times 8 \times 2

Multiply the terms

88 \times 2

Multiply the numbers

176

x^{7} \times 176

Use the commutative property to reorder the terms

176 x^{7}

176 x^{7} - 8 = 0

Move the constant to the right-hand side and change its sign

176 x^{7} = 0 + 8

Removing 0 doesn't change the value,so remove it from the expression

176 x^{7} = 8

Divide both sides

\frac{176 x ^{7}}{176} = \frac{8}{176}

Divide the numbers

x^{7} = \frac{8}{176}

Cancel out the common factor 8

x^{7} = \frac{1}{22}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 \frac{1}{22}

Calculate

x = 7 \frac{1}{22}

Solution

More Steps

Evaluate

7 \frac{1}{22}

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

\frac{7 1}{7 22}

Simplify the radical expression

\frac{1}{7 22}

Multiply by the Conjugate

\frac{7 2 2 ^{6}}{7 22 \times 7 2 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

722 \times 7 2 2^{6}

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

7 22 \times 2 2^{6}

Calculate the product

7 2 2^{7}

Reduce the index of the radical and exponent with 7

22

\frac{7 2 2 ^{6}}{22}

x = \frac{7 2 2 ^{6}}{22}

Alternative Form

x \approx 0.643021

Show Solution