Solve b^609-3477500

Question

Simplify the expression

9 b^{6} - 3477500

Evaluate

b^{6} \times 9 - 3477500

Solution

9 b^{6} - 3477500

Show Solution

b_{1} = - \frac{6 281677500}{3}, b_{2} = \frac{6 281677500}{3}

Alternative Form

b_{1} \approx - 8.534356, b_{2} \approx 8.534356

Evaluate

b^{6} \times 9 - 3477500

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

b^{6} \times 9 - 3477500 = 0

Use the commutative property to reorder the terms

9 b^{6} - 3477500 = 0

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

9 b^{6} = 0 + 3477500

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

9 b^{6} = 3477500

Divide both sides

\frac{9 b ^{6}}{9} = \frac{3477500}{9}

Divide the numbers

b^{6} = \frac{3477500}{9}

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

b = \pm 6 \frac{3477500}{9}

Simplify the expression

More Steps

Evaluate

6 \frac{3477500}{9}

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

\frac{6 3477500}{6 9}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{6 3477500}{3 3}

Multiply by the Conjugate

\frac{6 3477500 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{6 3477500 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

63477500 \times 39

Use n a = mn a^{m} to expand the expression

63477500 \times 6 9^{2}

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

6 3477500 \times 9^{2}

Calculate the product

6281677500

\frac{6 281677500}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{6 281677500}{3}

b = \pm \frac{6 281677500}{3}

Separate the equation into 2 possible cases

b = \frac{6 281677500}{3} b = - \frac{6 281677500}{3}

Solution

b_{1} = - \frac{6 281677500}{3}, b_{2} = \frac{6 281677500}{3}

Alternative Form

b_{1} \approx - 8.534356, b_{2} \approx 8.534356

Show Solution