Solve (|7p^4|)/8 =3

Question

Solve the equation

p_{1} = - \frac{4 8232}{7}, p_{2} = \frac{4 8232}{7}

Alternative Form

p_{1} \approx - 1.36075, p_{2} \approx 1.36075

Evaluate

\frac{7 p ^{4}}{8} = 3

When the expression in absolute value bars is not negative, remove the bars

\frac{7 p ^{4}}{8} = 3

Cross multiply

7 p^{4} = 8 \times 3

Simplify the equation

7 p^{4} = 24

Divide both sides

\frac{7 p ^{4}}{7} = \frac{24}{7}

Divide the numbers

p^{4} = \frac{24}{7}

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

p = \pm 4 \frac{24}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{24}{7}

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

\frac{4 24}{4 7}

Multiply by the Conjugate

\frac{4 24 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 24 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

424 \times 4343

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

4 24 \times 343

Calculate the product

48232

\frac{4 8232}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 8232}{7}

p = \pm \frac{4 8232}{7}

Separate the equation into 2 possible cases

p = \frac{4 8232}{7} p = - \frac{4 8232}{7}

Solution

p_{1} = - \frac{4 8232}{7}, p_{2} = \frac{4 8232}{7}

Alternative Form

p_{1} \approx - 1.36075, p_{2} \approx 1.36075

Show Solution