Solve dd^6621-100

Question

Simplify the expression

621 d^{7} - 100

Evaluate

d \times d^{6} \times 621 - 100

Solution

More Steps

Evaluate

d \times d^{6} \times 621

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 621

Add the numbers

d^{7} \times 621

Use the commutative property to reorder the terms

621 d^{7}

621 d^{7} - 100

Show Solution

d = \frac{7 100 \times 62 1 ^{6}}{621}

Alternative Form

d \approx 0.770373

Evaluate

d \times d^{6} \times 621 - 100

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

d \times d^{6} \times 621 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{6} \times 621

Multiply the terms with the same base by adding their exponents

d^{1 + 6} \times 621

Add the numbers

d^{7} \times 621

Use the commutative property to reorder the terms

621 d^{7}

621 d^{7} - 100 = 0

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

621 d^{7} = 0 + 100

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

621 d^{7} = 100

Divide both sides

\frac{621 d ^{7}}{621} = \frac{100}{621}

Divide the numbers

d^{7} = \frac{100}{621}

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

7 d^{7} = 7 \frac{100}{621}

Calculate

d = 7 \frac{100}{621}

Solution

More Steps

Evaluate

7 \frac{100}{621}

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

\frac{7 100}{7 621}

Multiply by the Conjugate

\frac{7 100 \times 7 62 1 ^{6}}{7 621 \times 7 62 1 ^{6}}

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

\frac{7 100 \times 62 1 ^{6}}{7 621 \times 7 62 1 ^{6}}

Multiply the numbers

More Steps

Evaluate

7621 \times 7 62 1^{6}

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

7 621 \times 62 1^{6}

Calculate the product

7 62 1^{7}

Reduce the index of the radical and exponent with 7

621

\frac{7 100 \times 62 1 ^{6}}{621}

d = \frac{7 100 \times 62 1 ^{6}}{621}

Alternative Form

d \approx 0.770373

Show Solution