Solve 8t^6 ( -4t) - 7

Question

Simplify the expression

- 32 t^{7} - 7

Evaluate

8 t^{6} (- 4 t) - 7

Solution

More Steps

Evaluate

8 t^{6} (- 4 t)

Rewrite the expression

- 8 t^{6} \times 4 t

Multiply the terms

- 32 t^{6} \times t

Multiply the terms with the same base by adding their exponents

- 32 t^{6 + 1}

Add the numbers

- 32 t^{7}

- 32 t^{7} - 7

Show Solution

Find the roots

t = - \frac{7 28}{2}

Alternative Form

t \approx - 0.804835

Evaluate

8 t^{6} (- 4 t) - 7

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

8 t^{6} (- 4 t) - 7 = 0

Multiply

More Steps

Multiply the terms

8 t^{6} (- 4 t)

Rewrite the expression

- 8 t^{6} \times 4 t

Multiply the terms

- 32 t^{6} \times t

Multiply the terms with the same base by adding their exponents

- 32 t^{6 + 1}

Add the numbers

- 32 t^{7}

- 32 t^{7} - 7 = 0

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

- 32 t^{7} = 0 + 7

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

- 32 t^{7} = 7

Change the signs on both sides of the equation

32 t^{7} = - 7

Divide both sides

\frac{32 t ^{7}}{32} = \frac{- 7}{32}

Divide the numbers

t^{7} = \frac{- 7}{32}

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

t^{7} = - \frac{7}{32}

Take the 7 -th root on both sides of the equation

7 t^{7} = 7 - \frac{7}{32}

Calculate

t = 7 - \frac{7}{32}

Solution

More Steps

Evaluate

7 - \frac{7}{32}

An odd root of a negative radicand is always a negative

- 7 \frac{7}{32}

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

- \frac{7 7}{7 32}

Multiply by the Conjugate

\frac{- 7 7 \times 7 3 2 ^{6}}{7 32 \times 7 3 2 ^{6}}

Simplify

\frac{- 7 7 \times 2 ^{4} 7 4}{7 32 \times 7 3 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

- 77 \times 2^{4} 74

Multiply the terms

- 728 \times 2^{4}

Use the commutative property to reorder the terms

- 2^{4} 728

\frac{- 2 ^{4} 7 28}{7 32 \times 7 3 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

732 \times 7 3 2^{6}

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

7 32 \times 3 2^{6}

Calculate the product

7 3 2^{7}

Transform the expression

7 2^{35}

Reduce the index of the radical and exponent with 7

2^{5}

\frac{- 2 ^{4} 7 28}{2 ^{5}}

Reduce the fraction

\frac{- 7 28}{2}

Calculate

- \frac{7 28}{2}

t = - \frac{7 28}{2}

Alternative Form

t \approx - 0.804835

Show Solution