Solve dd^68-185e-0

Question

Simplify the expression

8 d^{7} - 185 e

Evaluate

d \times d^{6} \times 8 - 185 e - 0

Multiply

More Steps

Multiply the terms

d \times d^{6} \times 8

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 8

Add the numbers

d^{7} \times 8

Use the commutative property to reorder the terms

8 d^{7}

8 d^{7} - 185 e - 0

Solution

8 d^{7} - 185 e

Show Solution

Find the roots

d = \frac{7 2960 e}{2}

Alternative Form

d \approx 1.806803

Evaluate

d \times d^{6} \times 8 - 185 e - 0

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

d \times d^{6} \times 8 - 185 e - 0 = 0

Multiply

More Steps

Multiply the terms

d \times d^{6} \times 8

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 8

Add the numbers

d^{7} \times 8

Use the commutative property to reorder the terms

8 d^{7}

8 d^{7} - 185 e - 0 = 0

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

8 d^{7} - 185 e = 0

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

8 d^{7} = 0 + 185 e

Add the terms

8 d^{7} = 185 e

Divide both sides

\frac{8 d ^{7}}{8} = \frac{185 e}{8}

Divide the numbers

d^{7} = \frac{185 e}{8}

Take the 7 -th root on both sides of the equation

7 d^{7} = 7 \frac{185 e}{8}

Calculate

d = 7 \frac{185 e}{8}

Solution

More Steps

Evaluate

7 \frac{185 e}{8}

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

\frac{7 185 e}{7 8}

Multiply by the Conjugate

\frac{7 185 e \times 7 8 ^{6}}{7 8 \times 7 8 ^{6}}

Simplify

\frac{7 185 e \times 2 ^{2} 7 16}{7 8 \times 7 8 ^{6}}

Multiply the numbers

More Steps

Evaluate

7 185 e \times 2^{2} 716

Multiply the terms

7 2960 e \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 7 2960 e

\frac{2 ^{2} 7 2960 e}{7 8 \times 7 8 ^{6}}

Multiply the numbers

More Steps

Evaluate

78 \times 7 8^{6}

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

7 8 \times 8^{6}

Calculate the product

7 8^{7}

Transform the expression

7 2^{21}

Reduce the index of the radical and exponent with 7

2^{3}

\frac{2 ^{2} 7 2960 e}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

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

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{7 2960 e}{2}

d = \frac{7 2960 e}{2}

Alternative Form

d \approx 1.806803

Show Solution