Solve p^63-e1 - ScanMath

Question

Simplify the expression

3 p^{6} - e

Evaluate

p^{6} \times 3 - e \times 1

Use the commutative property to reorder the terms

3 p^{6} - e \times 1

Solution

3 p^{6} - e

Show Solution

p_{1} = - \frac{6 243 e}{3}, p_{2} = \frac{6 243 e}{3}

Alternative Form

p_{1} \approx - 0.983699, p_{2} \approx 0.983699

Evaluate

p^{6} \times 3 - e \times 1

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

p^{6} \times 3 - e \times 1 = 0

Use the commutative property to reorder the terms

3 p^{6} - e \times 1 = 0

Multiply the numbers

3 p^{6} - e = 0

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

3 p^{6} = 0 + e

Add the terms

3 p^{6} = e

Divide both sides

\frac{3 p ^{6}}{3} = \frac{e}{3}

Divide the numbers

p^{6} = \frac{e}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

p = \pm 6 \frac{e}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{e}{3}

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

\frac{6 e}{6 3}

Multiply by the Conjugate

\frac{6 e \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 e \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

6 e \times 6243

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

6 e \times 243

Calculate the product

6 243 e

\frac{6 243 e}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{6 243 e}{3}

p = \pm \frac{6 243 e}{3}

Separate the equation into 2 possible cases

p = \frac{6 243 e}{3} p = - \frac{6 243 e}{3}

Solution

p_{1} = - \frac{6 243 e}{3}, p_{2} = \frac{6 243 e}{3}

Alternative Form

p_{1} \approx - 0.983699, p_{2} \approx 0.983699

Show Solution