Solve 24-200 d^5100

Question

Simplify the expression

24 - 20000 d^{5}

Evaluate

24 - 200 d^{5} \times 100

Solution

24 - 20000 d^{5}

Show Solution

8 (3 - 2500 d^{5})

Evaluate

24 - 200 d^{5} \times 100

Multiply the terms

24 - 20000 d^{5}

Solution

8 (3 - 2500 d^{5})

Show Solution

d = \frac{5 3 \times 5 0 ^{3}}{50}

Alternative Form

d \approx 0.260517

Evaluate

24 - 200 d^{5} \times 100

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

24 - 200 d^{5} \times 100 = 0

Multiply the terms

24 - 20000 d^{5} = 0

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

- 20000 d^{5} = 0 - 24

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

- 20000 d^{5} = - 24

Change the signs on both sides of the equation

20000 d^{5} = 24

Divide both sides

\frac{20000 d ^{5}}{20000} = \frac{24}{20000}

Divide the numbers

d^{5} = \frac{24}{20000}

Cancel out the common factor 8

d^{5} = \frac{3}{2500}

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

5 d^{5} = 5 \frac{3}{2500}

Calculate

d = 5 \frac{3}{2500}

Solution

More Steps

Evaluate

5 \frac{3}{2500}

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

\frac{5 3}{5 2500}

Multiply by the Conjugate

\frac{5 3 \times 5 250 0 ^{4}}{5 2500 \times 5 250 0 ^{4}}

Simplify

\frac{5 3 \times 50 5 5 0 ^{3}}{5 2500 \times 5 250 0 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 50 5 5 0^{3}

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

5 3 \times 5 0^{3} \times 50

Use the commutative property to reorder the terms

50 5 3 \times 5 0^{3}

\frac{50 5 3 \times 5 0 ^{3}}{5 2500 \times 5 250 0 ^{4}}

Multiply the numbers

More Steps

Evaluate

52500 \times 5 250 0^{4}

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

5 2500 \times 250 0^{4}

Calculate the product

5 250 0^{5}

Transform the expression

5 5 0^{10}

Reduce the index of the radical and exponent with 5

5 0^{2}

\frac{50 5 3 \times 5 0 ^{3}}{5 0 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{50}{5 0 ^{2}}

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

\frac{1}{5 0 ^{2 - 1}}

Subtract the terms

\frac{1}{5 0 ^{1}}

Simplify

\frac{1}{50}

\frac{5 3 \times 5 0 ^{3}}{50}

d = \frac{5 3 \times 5 0 ^{3}}{50}

Alternative Form

d \approx 0.260517

Show Solution