Solve dd^6610-100

Question

Simplify the expression

610 d^{7} - 100

Evaluate

d \times d^{6} \times 610 - 100

Solution

More Steps

Evaluate

d \times d^{6} \times 610

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 610

Add the numbers

d^{7} \times 610

Use the commutative property to reorder the terms

610 d^{7}

610 d^{7} - 100

Show Solution

10 (61 d^{7} - 10)

Evaluate

d \times d^{6} \times 610 - 100

Multiply

More Steps

Evaluate

d \times d^{6} \times 610

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 610

Add the numbers

d^{7} \times 610

Use the commutative property to reorder the terms

610 d^{7}

610 d^{7} - 100

Solution

10 (61 d^{7} - 10)

Show Solution

d = \frac{7 10 \times 6 1 ^{6}}{61}

Alternative Form

d \approx 0.772343

Evaluate

d \times d^{6} \times 610 - 100

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

d \times d^{6} \times 610 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{6} \times 610

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 610

Add the numbers

d^{7} \times 610

Use the commutative property to reorder the terms

610 d^{7}

610 d^{7} - 100 = 0

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

610 d^{7} = 0 + 100

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

610 d^{7} = 100

Divide both sides

\frac{610 d ^{7}}{610} = \frac{100}{610}

Divide the numbers

d^{7} = \frac{100}{610}

Cancel out the common factor 10

d^{7} = \frac{10}{61}

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

7 d^{7} = 7 \frac{10}{61}

Calculate

d = 7 \frac{10}{61}

Solution

More Steps

Evaluate

7 \frac{10}{61}

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

\frac{7 10}{7 61}

Multiply by the Conjugate

\frac{7 10 \times 7 6 1 ^{6}}{7 61 \times 7 6 1 ^{6}}

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

\frac{7 10 \times 6 1 ^{6}}{7 61 \times 7 6 1 ^{6}}

Multiply the numbers

More Steps

Evaluate

761 \times 7 6 1^{6}

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

7 61 \times 6 1^{6}

Calculate the product

7 6 1^{7}

Reduce the index of the radical and exponent with 7

61

\frac{7 10 \times 6 1 ^{6}}{61}

d = \frac{7 10 \times 6 1 ^{6}}{61}

Alternative Form

d \approx 0.772343

Show Solution