Solve 54902-768-49(b^5)

Question

Simplify the expression

54134 - 49 b^{5}

Evaluate

54902 - 768 - 49 b^{5}

Solution

54134 - 49 b^{5}

Show Solution

b = \frac{5 18567962}{7}

Alternative Form

b \approx 4.061204

Evaluate

54902 - 768 - 49 (b^{5})

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

54902 - 768 - 49 (b^{5}) = 0

Calculate

54902 - 768 - 49 b^{5} = 0

Subtract the numbers

54134 - 49 b^{5} = 0

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

- 49 b^{5} = 0 - 54134

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

- 49 b^{5} = - 54134

Change the signs on both sides of the equation

49 b^{5} = 54134

Divide both sides

\frac{49 b ^{5}}{49} = \frac{54134}{49}

Divide the numbers

b^{5} = \frac{54134}{49}

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

5 b^{5} = 5 \frac{54134}{49}

Calculate

b = 5 \frac{54134}{49}

Solution

More Steps

Evaluate

5 \frac{54134}{49}

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

\frac{5 54134}{5 49}

Multiply by the Conjugate

\frac{5 54134 \times 5 4 9 ^{4}}{5 49 \times 5 4 9 ^{4}}

Simplify

\frac{5 54134 \times 7 5 343}{5 49 \times 5 4 9 ^{4}}

Multiply the numbers

More Steps

Evaluate

554134 \times 75343

Multiply the terms

518567962 \times 7

Use the commutative property to reorder the terms

7518567962

\frac{7 5 18567962}{5 49 \times 5 4 9 ^{4}}

Multiply the numbers

More Steps

Evaluate

549 \times 5 4 9^{4}

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

5 49 \times 4 9^{4}

Calculate the product

5 4 9^{5}

Transform the expression

5 7^{10}

Reduce the index of the radical and exponent with 5

7^{2}

\frac{7 5 18567962}{7 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{7}{7 ^{2}}

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

\frac{1}{7 ^{2 - 1}}

Subtract the terms

\frac{1}{7 ^{1}}

Simplify

\frac{1}{7}

\frac{5 18567962}{7}

b = \frac{5 18567962}{7}

Alternative Form

b \approx 4.061204

Show Solution