Solve t^3/3 - 3t^2 8t^4

Question

Simplify the expression

Solution

\frac{t ^{3} - 72 t ^{6}}{3}

Evaluate

\frac{t ^{3}}{3} - 3 t^{2} \times 8 t^{4}

Multiply

More Steps

Multiply the terms

3 t^{2} \times 8 t^{4}

Multiply the terms

24 t^{2} \times t^{4}

Multiply the terms with the same base by adding their exponents

24 t^{2 + 4}

Add the numbers

24 t^{6}

\frac{t ^{3}}{3} - 24 t^{6}

Reduce fractions to a common denominator

\frac{t ^{3}}{3} - \frac{24 t ^{6} \times 3}{3}

Write all numerators above the common denominator

\frac{t ^{3} - 24 t ^{6} \times 3}{3}

Solution

\frac{t ^{3} - 72 t ^{6}}{3}

Show Solution

Find the roots

Find the roots of the algebra expression

t_{1} = 0, t_{2} = \frac{3 3}{6}

Alternative Form

t_{1} = 0, t_{2} \approx 0.240375

Evaluate

\frac{t ^{3}}{3} - 3 t^{2} \times 8 t^{4}

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

\frac{t ^{3}}{3} - 3 t^{2} \times 8 t^{4} = 0

Multiply

More Steps

Multiply the terms

3 t^{2} \times 8 t^{4}

Multiply the terms

24 t^{2} \times t^{4}

Multiply the terms with the same base by adding their exponents

24 t^{2 + 4}

Add the numbers

24 t^{6}

\frac{t ^{3}}{3} - 24 t^{6} = 0

Subtract the terms

More Steps

Simplify

\frac{t ^{3}}{3} - 24 t^{6}

Reduce fractions to a common denominator

\frac{t ^{3}}{3} - \frac{24 t ^{6} \times 3}{3}

Write all numerators above the common denominator

\frac{t ^{3} - 24 t ^{6} \times 3}{3}

Multiply the terms

\frac{t ^{3} - 72 t ^{6}}{3}

\frac{t ^{3} - 72 t ^{6}}{3} = 0

Simplify

t^{3} - 72 t^{6} = 0

Factor the expression

t^{3} (1 - 72 t^{3}) = 0

Separate the equation into 2 possible cases

t^{3} = 0 1 - 72 t^{3} = 0

The only way a power can be 0 is when the base equals 0

t = 0 1 - 72 t^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 72 t^{3} = 0

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

- 72 t^{3} = 0 - 1

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

- 72 t^{3} = - 1

Change the signs on both sides of the equation

72 t^{3} = 1

Divide both sides

\frac{72 t ^{3}}{72} = \frac{1}{72}

Divide the numbers

t^{3} = \frac{1}{72}

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

3 t^{3} = 3 \frac{1}{72}

Calculate

t = 3 \frac{1}{72}

Simplify the root

More Steps

Evaluate

3 \frac{1}{72}

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

\frac{3 1}{3 72}

Simplify the radical expression

\frac{1}{3 72}

Simplify the radical expression

\frac{1}{2 3 9}

Multiply by the Conjugate

\frac{3 9 ^{2}}{2 3 9 \times 3 9 ^{2}}

Simplify

\frac{3 3 3}{2 3 9 \times 3 9 ^{2}}

Multiply the numbers

\frac{3 3 3}{18}

Cancel out the common factor 3

\frac{3 3}{6}

t = \frac{3 3}{6}

t = 0 t = \frac{3 3}{6}

Solution

t_{1} = 0, t_{2} = \frac{3 3}{6}

Alternative Form

t_{1} = 0, t_{2} \approx 0.240375

Show Solution

T^3/3 3t^2 8t^4

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression