Solve t^6063-ｔ5

Question

Simplify the expression

63 t^{6} - 5 t

Evaluate

t^{6} \times 63 - t \times 5

Use the commutative property to reorder the terms

63 t^{6} - t \times 5

Solution

63 t^{6} - 5 t

Show Solution

t (63 t^{5} - 5)

Evaluate

t^{6} \times 63 - t \times 5

Use the commutative property to reorder the terms

63 t^{6} - t \times 5

Use the commutative property to reorder the terms

63 t^{6} - 5 t

Rewrite the expression

t \times 63 t^{5} - t \times 5

Solution

t (63 t^{5} - 5)

Show Solution

t_{1} = 0, t_{2} = \frac{5 5 \times 6 3 ^{4}}{63}

Alternative Form

t_{1} = 0, t_{2} \approx 0.602457

Evaluate

t^{6} \times 63 - t \times 5

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

t^{6} \times 63 - t \times 5 = 0

Use the commutative property to reorder the terms

63 t^{6} - t \times 5 = 0

Use the commutative property to reorder the terms

63 t^{6} - 5 t = 0

Factor the expression

t (63 t^{5} - 5) = 0

Separate the equation into 2 possible cases

t = 0 63 t^{5} - 5 = 0

Solve the equation

More Steps

Evaluate

63 t^{5} - 5 = 0

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

63 t^{5} = 0 + 5

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

63 t^{5} = 5

Divide both sides

\frac{63 t ^{5}}{63} = \frac{5}{63}

Divide the numbers

t^{5} = \frac{5}{63}

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

5 t^{5} = 5 \frac{5}{63}

Calculate

t = 5 \frac{5}{63}

Simplify the root

More Steps

Evaluate

5 \frac{5}{63}

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

\frac{5 5}{5 63}

Multiply by the Conjugate

\frac{5 5 \times 5 6 3 ^{4}}{5 63 \times 5 6 3 ^{4}}

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

\frac{5 5 \times 6 3 ^{4}}{5 63 \times 5 6 3 ^{4}}

Multiply the numbers

\frac{5 5 \times 6 3 ^{4}}{63}

t = \frac{5 5 \times 6 3 ^{4}}{63}

t = 0 t = \frac{5 5 \times 6 3 ^{4}}{63}

Solution

t_{1} = 0, t_{2} = \frac{5 5 \times 6 3 ^{4}}{63}

Alternative Form

t_{1} = 0, t_{2} \approx 0.602457

Show Solution