Solve dd^4008-10 - ScanMath

Question

Simplify the expression

8 d^{5} - 10

Evaluate

d \times d^{4} \times 8 - 10

Solution

More Steps

Evaluate

d \times d^{4} \times 8

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 8

Add the numbers

d^{5} \times 8

Use the commutative property to reorder the terms

8 d^{5}

8 d^{5} - 10

Show Solution

Factor the expression

2 (4 d^{5} - 5)

Evaluate

d \times d^{4} \times 8 - 10

Multiply

More Steps

Evaluate

d \times d^{4} \times 8

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 8

Add the numbers

d^{5} \times 8

Use the commutative property to reorder the terms

8 d^{5}

8 d^{5} - 10

Solution

2 (4 d^{5} - 5)

Show Solution

Find the roots

d = \frac{5 40}{2}

Alternative Form

d \approx 1.04564

Evaluate

d \times d^{4} \times 8 - 10

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

d \times d^{4} \times 8 - 10 = 0

Multiply

More Steps

Multiply the terms

d \times d^{4} \times 8

Multiply the terms with the same base by adding their exponents

d^{1 + 4} \times 8

Add the numbers

d^{5} \times 8

Use the commutative property to reorder the terms

8 d^{5}

8 d^{5} - 10 = 0

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

8 d^{5} = 0 + 10

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

8 d^{5} = 10

Divide both sides

\frac{8 d ^{5}}{8} = \frac{10}{8}

Divide the numbers

d^{5} = \frac{10}{8}

Cancel out the common factor 2

d^{5} = \frac{5}{4}

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

5 d^{5} = 5 \frac{5}{4}

Calculate

d = 5 \frac{5}{4}

Solution

More Steps

Evaluate

5 \frac{5}{4}

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

\frac{5 5}{5 4}

Multiply by the Conjugate

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

Simplify

\frac{5 5 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

55 \times 258

Multiply the terms

540 \times 2

Use the commutative property to reorder the terms

2540

\frac{2 5 40}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 40}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 40}{2}

d = \frac{5 40}{2}

Alternative Form

d \approx 1.04564

Show Solution