Solve -16t^2 32t^3 = y

Question

Solve the equation

Solve for t

Solve for y

t = - \frac{5 2 y}{4}

Evaluate

- 16 t^{2} \times 32 t^{3} = y

Multiply

More Steps

Evaluate

- 16 t^{2} \times 32 t^{3}

Multiply the terms

- 512 t^{2} \times t^{3}

Multiply the terms with the same base by adding their exponents

- 512 t^{2 + 3}

Add the numbers

- 512 t^{5}

- 512 t^{5} = y

Change the signs on both sides of the equation

512 t^{5} = - y

Divide both sides

\frac{512 t ^{5}}{512} = \frac{- y}{512}

Divide the numbers

t^{5} = \frac{- y}{512}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

t^{5} = - \frac{y}{512}

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

5 t^{5} = 5 - \frac{y}{512}

Calculate

t = 5 - \frac{y}{512}

Solution

More Steps

Evaluate

5 - \frac{y}{512}

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

\frac{5 - y}{5 512}

Simplify the radical expression

More Steps

Evaluate

5512

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

5 32 \times 16

Write the number in exponential form with the base of 2

5 2^{5} \times 16

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

5 2^{5} \times 516

Reduce the index of the radical and exponent with 5

2516

\frac{5 - y}{2 5 16}

Multiply by the Conjugate

\frac{5 - y \times 5 1 6 ^{4}}{2 5 16 \times 5 1 6 ^{4}}

Calculate

\frac{5 - y \times 5 1 6 ^{4}}{2 \times 2 ^{4}}

Calculate

More Steps

Evaluate

5 - y \times 5 1 6^{4}

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

5 - y \times 1 6^{4}

Calculate the product

5 - 1 6^{4} y

An odd root of a negative radicand is always a negative

- 5 1 6^{4} y

Simplify the radical expression

- 8 5 2 y

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

Calculate

\frac{- 8 5 2 y}{2 ^{5}}

Divide the terms

More Steps

Evaluate

\frac{- 8}{2 ^{5}}

Rewrite the expression

\frac{- 8}{8 \times 4}

Cancel out the common factor 8

\frac{- 1}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{4}

\frac{- 5 2 y}{4}

Calculate

- \frac{5 2 y}{4}

t = - \frac{5 2 y}{4}

Show Solution