Solve dd^4756-84 - ScanMath

Question

Simplify the expression

756 d^{5} - 84

Evaluate

d \times d^{4} \times 756 - 84

Solution

More Steps

Evaluate

d \times d^{4} \times 756

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 756

Add the numbers

d^{5} \times 756

Use the commutative property to reorder the terms

756 d^{5}

756 d^{5} - 84

Show Solution

Factor the expression

84 (9 d^{5} - 1)

Evaluate

d \times d^{4} \times 756 - 84

Multiply

More Steps

Evaluate

d \times d^{4} \times 756

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 756

Add the numbers

d^{5} \times 756

Use the commutative property to reorder the terms

756 d^{5}

756 d^{5} - 84

Solution

84 (9 d^{5} - 1)

Show Solution

Find the roots

d = \frac{5 27}{3}

Alternative Form

d \approx 0.644394

Evaluate

d \times d^{4} \times 756 - 84

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

d \times d^{4} \times 756 - 84 = 0

Multiply

More Steps

Multiply the terms

d \times d^{4} \times 756

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 756

Add the numbers

d^{5} \times 756

Use the commutative property to reorder the terms

756 d^{5}

756 d^{5} - 84 = 0

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

756 d^{5} = 0 + 84

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

756 d^{5} = 84

Divide both sides

\frac{756 d ^{5}}{756} = \frac{84}{756}

Divide the numbers

d^{5} = \frac{84}{756}

Cancel out the common factor 84

d^{5} = \frac{1}{9}

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

5 d^{5} = 5 \frac{1}{9}

Calculate

d = 5 \frac{1}{9}

Solution

More Steps

Evaluate

5 \frac{1}{9}

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

\frac{5 1}{5 9}

Simplify the radical expression

\frac{1}{5 9}

Multiply by the Conjugate

\frac{5 9 ^{4}}{5 9 \times 5 9 ^{4}}

Simplify

\frac{3 5 27}{5 9 \times 5 9 ^{4}}

Multiply the numbers

More Steps

Evaluate

59 \times 5 9^{4}

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

5 9 \times 9^{4}

Calculate the product

5 9^{5}

Transform the expression

5 3^{10}

Reduce the index of the radical and exponent with 5

3^{2}

\frac{3 5 27}{3 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{3}{3 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{3 ^{2 - 1}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{5 27}{3}

d = \frac{5 27}{3}

Alternative Form

d \approx 0.644394

Show Solution