Solve dd^6618-100

Question

Simplify the expression

618 d^{7} - 100

Evaluate

d \times d^{6} \times 618 - 100

Solution

More Steps

Evaluate

d \times d^{6} \times 618

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 618

Add the numbers

d^{7} \times 618

Use the commutative property to reorder the terms

618 d^{7}

618 d^{7} - 100

Show Solution

2 (309 d^{7} - 50)

Evaluate

d \times d^{6} \times 618 - 100

Multiply

More Steps

Evaluate

d \times d^{6} \times 618

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 618

Add the numbers

d^{7} \times 618

Use the commutative property to reorder the terms

618 d^{7}

618 d^{7} - 100

Solution

2 (309 d^{7} - 50)

Show Solution

d = \frac{7 50 \times 30 9 ^{6}}{309}

Alternative Form

d \approx 0.770906

Evaluate

d \times d^{6} \times 618 - 100

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

d \times d^{6} \times 618 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{6} \times 618

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 618

Add the numbers

d^{7} \times 618

Use the commutative property to reorder the terms

618 d^{7}

618 d^{7} - 100 = 0

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

618 d^{7} = 0 + 100

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

618 d^{7} = 100

Divide both sides

\frac{618 d ^{7}}{618} = \frac{100}{618}

Divide the numbers

d^{7} = \frac{100}{618}

Cancel out the common factor 2

d^{7} = \frac{50}{309}

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

7 d^{7} = 7 \frac{50}{309}

Calculate

d = 7 \frac{50}{309}

Solution

More Steps

Evaluate

7 \frac{50}{309}

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

\frac{7 50}{7 309}

Multiply by the Conjugate

\frac{7 50 \times 7 30 9 ^{6}}{7 309 \times 7 30 9 ^{6}}

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

\frac{7 50 \times 30 9 ^{6}}{7 309 \times 7 30 9 ^{6}}

Multiply the numbers

More Steps

Evaluate

7309 \times 7 30 9^{6}

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

7 309 \times 30 9^{6}

Calculate the product

7 30 9^{7}

Reduce the index of the radical and exponent with 7

309

\frac{7 50 \times 30 9 ^{6}}{309}

d = \frac{7 50 \times 30 9 ^{6}}{309}

Alternative Form

d \approx 0.770906

Show Solution