Solve 12198452b^2b=180

Question

Solve the equation

b = \frac{3 45 \times 889 1 ^{2}}{62237}

Alternative Form

b \approx 0.024528

Evaluate

12198452 b^{2} \times b = 180

Multiply

More Steps

Evaluate

12198452 b^{2} \times b

Multiply the terms with the same base by adding their exponents

12198452 b^{2 + 1}

Add the numbers

12198452 b^{3}

12198452 b^{3} = 180

Divide both sides

\frac{12198452 b ^{3}}{12198452} = \frac{180}{12198452}

Divide the numbers

b^{3} = \frac{180}{12198452}

Cancel out the common factor 4

b^{3} = \frac{45}{3049613}

Take the 3 -th root on both sides of the equation

3 b^{3} = 3 \frac{45}{3049613}

Calculate

b = 3 \frac{45}{3049613}

Solution

More Steps

Evaluate

3 \frac{45}{3049613}

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

\frac{3 45}{3 3049613}

Simplify the radical expression

More Steps

Evaluate

33049613

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

3 343 \times 8891

Write the number in exponential form with the base of 7

3 7^{3} \times 8891

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

3 7^{3} \times 38891

Reduce the index of the radical and exponent with 3

738891

\frac{3 45}{7 3 8891}

Multiply by the Conjugate

\frac{3 45 \times 3 889 1 ^{2}}{7 3 8891 \times 3 889 1 ^{2}}

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

\frac{3 45 \times 889 1 ^{2}}{7 3 8891 \times 3 889 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

738891 \times 3 889 1^{2}

Multiply the terms

7 \times 8891

Multiply the terms

62237

\frac{3 45 \times 889 1 ^{2}}{62237}

b = \frac{3 45 \times 889 1 ^{2}}{62237}

Alternative Form

b \approx 0.024528

Show Solution