Solve dd^4747-412

Question

Simplify the expression

747 d^{5} - 412

Evaluate

d \times d^{4} \times 747 - 412

Solution

More Steps

Evaluate

d \times d^{4} \times 747

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 747

Add the numbers

d^{5} \times 747

Use the commutative property to reorder the terms

747 d^{5}

747 d^{5} - 412

Show Solution

d = \frac{5 412 \times 74 7 ^{4}}{747}

Alternative Form

d \approx 0.8878

Evaluate

d \times d^{4} \times 747 - 412

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

d \times d^{4} \times 747 - 412 = 0

Multiply

More Steps

Multiply the terms

d \times d^{4} \times 747

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 747

Add the numbers

d^{5} \times 747

Use the commutative property to reorder the terms

747 d^{5}

747 d^{5} - 412 = 0

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

747 d^{5} = 0 + 412

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

747 d^{5} = 412

Divide both sides

\frac{747 d ^{5}}{747} = \frac{412}{747}

Divide the numbers

d^{5} = \frac{412}{747}

Take the 5 -th root on both sides of the equation

5 d^{5} = 5 \frac{412}{747}

Calculate

d = 5 \frac{412}{747}

Solution

More Steps

Evaluate

5 \frac{412}{747}

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

\frac{5 412}{5 747}

Multiply by the Conjugate

\frac{5 412 \times 5 74 7 ^{4}}{5 747 \times 5 74 7 ^{4}}

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

\frac{5 412 \times 74 7 ^{4}}{5 747 \times 5 74 7 ^{4}}

Multiply the numbers

More Steps

Evaluate

5747 \times 5 74 7^{4}

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

5 747 \times 74 7^{4}

Calculate the product

5 74 7^{5}

Reduce the index of the radical and exponent with 5

747

\frac{5 412 \times 74 7 ^{4}}{747}

d = \frac{5 412 \times 74 7 ^{4}}{747}

Alternative Form

d \approx 0.8878

Show Solution