Solve 6400 f^418-105

Question

Simplify the expression

115200 f^{4} - 105

Evaluate

6400 f^{4} \times 18 - 105

Solution

115200 f^{4} - 105

Show Solution

15 (7680 f^{4} - 7)

Evaluate

6400 f^{4} \times 18 - 105

Multiply the terms

115200 f^{4} - 105

Solution

15 (7680 f^{4} - 7)

Show Solution

f_{1} = - \frac{4 189000}{120}, f_{2} = \frac{4 189000}{120}

Alternative Form

f_{1} \approx - 0.173754, f_{2} \approx 0.173754

Evaluate

6400 f^{4} \times 18 - 105

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

6400 f^{4} \times 18 - 105 = 0

Multiply the terms

115200 f^{4} - 105 = 0

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

115200 f^{4} = 0 + 105

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

115200 f^{4} = 105

Divide both sides

\frac{115200 f ^{4}}{115200} = \frac{105}{115200}

Divide the numbers

f^{4} = \frac{105}{115200}

Cancel out the common factor 15

f^{4} = \frac{7}{7680}

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

f = \pm 4 \frac{7}{7680}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{7680}

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

\frac{4 7}{4 7680}

Simplify the radical expression

More Steps

Evaluate

47680

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

4 256 \times 30

Write the number in exponential form with the base of 4

4 4^{4} \times 30

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

4 4^{4} \times 430

Reduce the index of the radical and exponent with 4

4430

\frac{4 7}{4 4 30}

Multiply by the Conjugate

\frac{4 7 \times 4 3 0 ^{3}}{4 4 30 \times 4 3 0 ^{3}}

Simplify

\frac{4 7 \times 4 27000}{4 4 30 \times 4 3 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 427000

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

4 7 \times 27000

Calculate the product

4189000

\frac{4 189000}{4 4 30 \times 4 3 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

4430 \times 4 3 0^{3}

Multiply the terms

4 \times 30

Multiply the terms

120

\frac{4 189000}{120}

f = \pm \frac{4 189000}{120}

Separate the equation into 2 possible cases

f = \frac{4 189000}{120} f = - \frac{4 189000}{120}

Solution

f_{1} = - \frac{4 189000}{120}, f_{2} = \frac{4 189000}{120}

Alternative Form

f_{1} \approx - 0.173754, f_{2} \approx 0.173754

Show Solution