Solve 3000-3200 p^2p

Question

Simplify the expression

3000 - 3200 p^{3}

Evaluate

3000 - 3200 p^{2} \times p

Solution

More Steps

Evaluate

3200 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3200 p^{2 + 1}

Add the numbers

3200 p^{3}

3000 - 3200 p^{3}

Show Solution

Factor the expression

200 (15 - 16 p^{3})

Evaluate

3000 - 3200 p^{2} \times p

Multiply

More Steps

Evaluate

3200 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3200 p^{2 + 1}

Add the numbers

3200 p^{3}

3000 - 3200 p^{3}

Solution

200 (15 - 16 p^{3})

Show Solution

Find the roots

p = \frac{3 60}{4}

Alternative Form

p \approx 0.978717

Evaluate

3000 - 3200 p^{2} \times p

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

3000 - 3200 p^{2} \times p = 0

Multiply

More Steps

Multiply the terms

3200 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3200 p^{2 + 1}

Add the numbers

3200 p^{3}

3000 - 3200 p^{3} = 0

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

- 3200 p^{3} = 0 - 3000

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

- 3200 p^{3} = - 3000

Change the signs on both sides of the equation

3200 p^{3} = 3000

Divide both sides

\frac{3200 p ^{3}}{3200} = \frac{3000}{3200}

Divide the numbers

p^{3} = \frac{3000}{3200}

Cancel out the common factor 200

p^{3} = \frac{15}{16}

Take the 3 -th root on both sides of the equation

3 p^{3} = 3 \frac{15}{16}

Calculate

p = 3 \frac{15}{16}

Solution

More Steps

Evaluate

3 \frac{15}{16}

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

\frac{3 15}{3 16}

Simplify the radical expression

More Steps

Evaluate

316

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{3 15}{2 3 2}

Multiply by the Conjugate

\frac{3 15 \times 3 2 ^{2}}{2 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 15 \times 3 4}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 34

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

3 15 \times 4

Calculate the product

360

\frac{3 60}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 3 2^{2}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{3 60}{4}

p = \frac{3 60}{4}

Alternative Form

p \approx 0.978717

Show Solution