Solve dd^4746-412

Question

Simplify the expression

746 d^{5} - 412

Evaluate

d \times d^{4} \times 746 - 412

Solution

More Steps

Evaluate

d \times d^{4} \times 746

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 746

Add the numbers

d^{5} \times 746

Use the commutative property to reorder the terms

746 d^{5}

746 d^{5} - 412

Show Solution

2 (373 d^{5} - 206)

Evaluate

d \times d^{4} \times 746 - 412

Multiply

More Steps

Evaluate

d \times d^{4} \times 746

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 746

Add the numbers

d^{5} \times 746

Use the commutative property to reorder the terms

746 d^{5}

746 d^{5} - 412

Solution

2 (373 d^{5} - 206)

Show Solution

d = \frac{5 206 \times 37 3 ^{4}}{373}

Alternative Form

d \approx 0.888038

Evaluate

d \times d^{4} \times 746 - 412

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

d \times d^{4} \times 746 - 412 = 0

Multiply

More Steps

Multiply the terms

d \times d^{4} \times 746

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 746

Add the numbers

d^{5} \times 746

Use the commutative property to reorder the terms

746 d^{5}

746 d^{5} - 412 = 0

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

746 d^{5} = 0 + 412

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

746 d^{5} = 412

Divide both sides

\frac{746 d ^{5}}{746} = \frac{412}{746}

Divide the numbers

d^{5} = \frac{412}{746}

Cancel out the common factor 2

d^{5} = \frac{206}{373}

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

5 d^{5} = 5 \frac{206}{373}

Calculate

d = 5 \frac{206}{373}

Solution

More Steps

Evaluate

5 \frac{206}{373}

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

\frac{5 206}{5 373}

Multiply by the Conjugate

\frac{5 206 \times 5 37 3 ^{4}}{5 373 \times 5 37 3 ^{4}}

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

\frac{5 206 \times 37 3 ^{4}}{5 373 \times 5 37 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

5373 \times 5 37 3^{4}

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

5 373 \times 37 3^{4}

Calculate the product

5 37 3^{5}

Reduce the index of the radical and exponent with 5

373

\frac{5 206 \times 37 3 ^{4}}{373}

d = \frac{5 206 \times 37 3 ^{4}}{373}

Alternative Form

d \approx 0.888038

Show Solution