Solve dd^3111-100

Question

Simplify the expression

111 d^{4} - 100

Evaluate

d \times d^{3} \times 111 - 100

Solution

More Steps

Evaluate

d \times d^{3} \times 111

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 111

Add the numbers

d^{4} \times 111

Use the commutative property to reorder the terms

111 d^{4}

111 d^{4} - 100

Show Solution

d_{1} = - \frac{4 100 \times 11 1 ^{3}}{111}, d_{2} = \frac{4 100 \times 11 1 ^{3}}{111}

Alternative Form

d_{1} \approx - 0.974247, d_{2} \approx 0.974247

Evaluate

d \times d^{3} \times 111 - 100

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

d \times d^{3} \times 111 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 111

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 111

Add the numbers

d^{4} \times 111

Use the commutative property to reorder the terms

111 d^{4}

111 d^{4} - 100 = 0

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

111 d^{4} = 0 + 100

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

111 d^{4} = 100

Divide both sides

\frac{111 d ^{4}}{111} = \frac{100}{111}

Divide the numbers

d^{4} = \frac{100}{111}

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

d = \pm 4 \frac{100}{111}

Simplify the expression

More Steps

Evaluate

4 \frac{100}{111}

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

\frac{4 100}{4 111}

Simplify the radical expression

\frac{10}{4 111}

Multiply by the Conjugate

\frac{10 \times 4 11 1 ^{3}}{4 111 \times 4 11 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

10 \times 4 11 1^{3}

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

4 1 0^{2} \times 4 11 1^{3}

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

4 1 0^{2} \times 11 1^{3}

Calculate the product

4 100 \times 11 1^{3}

\frac{4 100 \times 11 1 ^{3}}{4 111 \times 4 11 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

4111 \times 4 11 1^{3}

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

4 111 \times 11 1^{3}

Calculate the product

4 11 1^{4}

Reduce the index of the radical and exponent with 4

111

\frac{4 100 \times 11 1 ^{3}}{111}

d = \pm \frac{4 100 \times 11 1 ^{3}}{111}

Separate the equation into 2 possible cases

d = \frac{4 100 \times 11 1 ^{3}}{111} d = - \frac{4 100 \times 11 1 ^{3}}{111}

Solution

d_{1} = - \frac{4 100 \times 11 1 ^{3}}{111}, d_{2} = \frac{4 100 \times 11 1 ^{3}}{111}

Alternative Form

d_{1} \approx - 0.974247, d_{2} \approx 0.974247

Show Solution