Solve b- b1 b^2 b^3 b^4 b^5 b^6 b7 b8 b9 b10 b

Question

Simplify the expression

b - 5040 b^{26}

Evaluate

b - b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Rewrite the expression in exponential form

b - b^{6} \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times 7 \times 8 \times 9 \times 10

Solution

More Steps

Multiply the terms

b^{6} \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times 7 \times 8 \times 9 \times 10

Rewrite the expression

b^{6} \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times 7 \times 8 \times 9 \times 10

Multiply the terms with the same base by adding their exponents

b^{6 + 2 + 3 + 4 + 5 + 6} \times 7 \times 8 \times 9 \times 10

Add the numbers

b^{26} \times 7 \times 8 \times 9 \times 10

Multiply the terms

More Steps

Evaluate

7 \times 8 \times 9 \times 10

Multiply the terms

56 \times 9 \times 10

Multiply the terms

504 \times 10

Multiply the numbers

5040

b^{26} \times 5040

Use the commutative property to reorder the terms

5040 b^{26}

b - 5040 b^{26}

Show Solution

Factor the expression

b (1 - 5040 b^{25})

Evaluate

b - b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Multiply the terms

More Steps

Evaluate

b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Rewrite the expression

b \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Multiply the terms with the same base by adding their exponents

b^{1 + 2 + 3 + 4 + 5 + 6 + 1 + 1 + 1 + 1 + 1} \times 7 \times 8 \times 9 \times 10

Add the numbers

b^{26} \times 7 \times 8 \times 9 \times 10

Multiply the terms

More Steps

Evaluate

7 \times 8 \times 9 \times 10

Multiply the terms

56 \times 9 \times 10

Multiply the terms

504 \times 10

Multiply the numbers

5040

b^{26} \times 5040

Use the commutative property to reorder the terms

5040 b^{26}

b - 5040 b^{26}

Rewrite the expression

b - b \times 5040 b^{25}

Solution

b (1 - 5040 b^{25})

Show Solution

Find the roots

b_{1} = 0, b_{2} = \frac{25 504 0 ^{24}}{5040}

Alternative Form

b_{1} = 0, b_{2} \approx 0.711054

Evaluate

b - b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

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

b - b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b = 0

Multiply the terms

More Steps

Multiply the terms

b \times 1 \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Rewrite the expression

b \times b^{2} \times b^{3} \times b^{4} \times b^{5} \times b^{6} \times b \times 7 b \times 8 b \times 9 b \times 10 b

Multiply the terms with the same base by adding their exponents

b^{1 + 2 + 3 + 4 + 5 + 6 + 1 + 1 + 1 + 1 + 1} \times 7 \times 8 \times 9 \times 10

Add the numbers

b^{26} \times 7 \times 8 \times 9 \times 10

Multiply the terms

More Steps

Evaluate

7 \times 8 \times 9 \times 10

Multiply the terms

56 \times 9 \times 10

Multiply the terms

504 \times 10

Multiply the numbers

5040

b^{26} \times 5040

Use the commutative property to reorder the terms

5040 b^{26}

b - 5040 b^{26} = 0

Factor the expression

b (1 - 5040 b^{25}) = 0

Separate the equation into 2 possible cases

b = 0 1 - 5040 b^{25} = 0

Solve the equation

More Steps

Evaluate

1 - 5040 b^{25} = 0

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

- 5040 b^{25} = 0 - 1

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

- 5040 b^{25} = - 1

Change the signs on both sides of the equation

5040 b^{25} = 1

Divide both sides

\frac{5040 b ^{25}}{5040} = \frac{1}{5040}

Divide the numbers

b^{25} = \frac{1}{5040}

Take the 25 -th root on both sides of the equation

25 b^{25} = 25 \frac{1}{5040}

Calculate

b = 25 \frac{1}{5040}

Simplify the root

More Steps

Evaluate

25 \frac{1}{5040}

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

\frac{25 1}{25 5040}

Simplify the radical expression

\frac{1}{25 5040}

Multiply by the Conjugate

\frac{25 504 0 ^{24}}{25 5040 \times 25 504 0 ^{24}}

Multiply the numbers

\frac{25 504 0 ^{24}}{5040}

b = \frac{25 504 0 ^{24}}{5040}

b = 0 b = \frac{25 504 0 ^{24}}{5040}

Solution

b_{1} = 0, b_{2} = \frac{25 504 0 ^{24}}{5040}

Alternative Form

b_{1} = 0, b_{2} \approx 0.711054

Show Solution