Solve 9 - 7b^5b^4b

Question

Simplify the expression

9 - 7 b^{10}

Evaluate

9 - 7 b^{5} \times b^{4} \times b

Solution

More Steps

Evaluate

7 b^{5} \times b^{4} \times b

Multiply the terms with the same base by adding their exponents

7 b^{5 + 4 + 1}

Add the numbers

7 b^{10}

9 - 7 b^{10}

Show Solution

b_{1} = - \frac{10 9 \times 7 ^{9}}{7}, b_{2} = \frac{10 9 \times 7 ^{9}}{7}

Alternative Form

b_{1} \approx - 1.02545, b_{2} \approx 1.02545

Evaluate

9 - 7 b^{5} \times b^{4} \times b

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

9 - 7 b^{5} \times b^{4} \times b = 0

Multiply

More Steps

Multiply the terms

7 b^{5} \times b^{4} \times b

Multiply the terms with the same base by adding their exponents

7 b^{5 + 4 + 1}

Add the numbers

7 b^{10}

9 - 7 b^{10} = 0

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

- 7 b^{10} = 0 - 9

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

- 7 b^{10} = - 9

Change the signs on both sides of the equation

7 b^{10} = 9

Divide both sides

\frac{7 b ^{10}}{7} = \frac{9}{7}

Divide the numbers

b^{10} = \frac{9}{7}

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

b = \pm 10 \frac{9}{7}

Simplify the expression

More Steps

Evaluate

10 \frac{9}{7}

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

\frac{10 9}{10 7}

Simplify the radical expression

More Steps

Evaluate

109

Write the number in exponential form with the base of 3

10 3^{2}

Reduce the index of the radical and exponent with 2

53

\frac{5 3}{10 7}

Multiply by the Conjugate

\frac{5 3 \times 10 7 ^{9}}{10 7 \times 10 7 ^{9}}

Multiply the numbers

More Steps

Evaluate

53 \times 10 7^{9}

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

10 3^{2} \times 10 7^{9}

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

10 3^{2} \times 7^{9}

Calculate the product

10 9 \times 7^{9}

\frac{10 9 \times 7 ^{9}}{10 7 \times 10 7 ^{9}}

Multiply the numbers

More Steps

Evaluate

107 \times 10 7^{9}

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

10 7 \times 7^{9}

Calculate the product

10 7^{10}

Reduce the index of the radical and exponent with 10

7

\frac{10 9 \times 7 ^{9}}{7}

b = \pm \frac{10 9 \times 7 ^{9}}{7}

Separate the equation into 2 possible cases

b = \frac{10 9 \times 7 ^{9}}{7} b = - \frac{10 9 \times 7 ^{9}}{7}

Solution

b_{1} = - \frac{10 9 \times 7 ^{9}}{7}, b_{2} = \frac{10 9 \times 7 ^{9}}{7}

Alternative Form

b_{1} \approx - 1.02545, b_{2} \approx 1.02545

Show Solution