Solve p^49-1001-300

Question

Simplify the expression

9 p^{4} - 1301

Evaluate

p^{4} \times 9 - 1001 - 300

Use the commutative property to reorder the terms

9 p^{4} - 1001 - 300

Solution

9 p^{4} - 1301

Show Solution

p_{1} = - \frac{4 11709}{3}, p_{2} = \frac{4 11709}{3}

Alternative Form

p_{1} \approx - 3.467438, p_{2} \approx 3.467438

Evaluate

p^{4} \times 9 - 1001 - 300

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

p^{4} \times 9 - 1001 - 300 = 0

Use the commutative property to reorder the terms

9 p^{4} - 1001 - 300 = 0

Subtract the numbers

9 p^{4} - 1301 = 0

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

9 p^{4} = 0 + 1301

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

9 p^{4} = 1301

Divide both sides

\frac{9 p ^{4}}{9} = \frac{1301}{9}

Divide the numbers

p^{4} = \frac{1301}{9}

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

p = \pm 4 \frac{1301}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{1301}{9}

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

\frac{4 1301}{4 9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4 1301}{3}

Multiply by the Conjugate

\frac{4 1301 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

41301 \times 3

Use n a = mn a^{m} to expand the expression

41301 \times 4 3^{2}

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

4 1301 \times 3^{2}

Calculate the product

411709

\frac{4 11709}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 11709}{3}

p = \pm \frac{4 11709}{3}

Separate the equation into 2 possible cases

p = \frac{4 11709}{3} p = - \frac{4 11709}{3}

Solution

p_{1} = - \frac{4 11709}{3}, p_{2} = \frac{4 11709}{3}

Alternative Form

p_{1} \approx - 3.467438, p_{2} \approx 3.467438

Show Solution