Solve 4x x^48-8 - ScanMath

Question

Simplify the expression

32 x^{5} - 8

Evaluate

4 x \times x^{4} \times 8 - 8

Solution

More Steps

Evaluate

4 x \times x^{4} \times 8

Multiply the terms

32 x \times x^{4}

Multiply the terms with the same base by adding their exponents

32 x^{1 + 4}

Add the numbers

32 x^{5}

32 x^{5} - 8

Show Solution

Factor the expression

8 (4 x^{5} - 1)

Evaluate

4 x \times x^{4} \times 8 - 8

Multiply

More Steps

Evaluate

4 x \times x^{4} \times 8

Multiply the terms

32 x \times x^{4}

Multiply the terms with the same base by adding their exponents

32 x^{1 + 4}

Add the numbers

32 x^{5}

32 x^{5} - 8

Solution

8 (4 x^{5} - 1)

Show Solution

Find the roots

x = \frac{5 8}{2}

Alternative Form

x \approx 0.757858

Evaluate

4 x \times x^{4} \times 8 - 8

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

4 x \times x^{4} \times 8 - 8 = 0

Multiply

More Steps

Multiply the terms

4 x \times x^{4} \times 8

Multiply the terms

32 x \times x^{4}

Multiply the terms with the same base by adding their exponents

32 x^{1 + 4}

Add the numbers

32 x^{5}

32 x^{5} - 8 = 0

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

32 x^{5} = 0 + 8

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

32 x^{5} = 8

Divide both sides

\frac{32 x ^{5}}{32} = \frac{8}{32}

Divide the numbers

x^{5} = \frac{8}{32}

Cancel out the common factor 8

x^{5} = \frac{1}{4}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{4}

Calculate

x = 5 \frac{1}{4}

Solution

More Steps

Evaluate

5 \frac{1}{4}

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

\frac{5 1}{5 4}

Simplify the radical expression

\frac{1}{5 4}

Multiply by the Conjugate

\frac{5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 8}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 8}{2}

x = \frac{5 8}{2}

Alternative Form

x \approx 0.757858

Show Solution