Solve p^54-6020-3

Question

Simplify the expression

Solution

4 p^{5} - 6023

Evaluate

p^{5} \times 4 - 6020 - 3

Use the commutative property to reorder the terms

4 p^{5} - 6020 - 3

Solution

4 p^{5} - 6023

Show Solution

Find the roots of the algebra expression

p = \frac{5 48184}{2}

Alternative Form

p \approx 4.320665

Evaluate

p^{5} \times 4 - 6020 - 3

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

p^{5} \times 4 - 6020 - 3 = 0

Use the commutative property to reorder the terms

4 p^{5} - 6020 - 3 = 0

Subtract the numbers

4 p^{5} - 6023 = 0

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

4 p^{5} = 0 + 6023

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

4 p^{5} = 6023

Divide both sides

\frac{4 p ^{5}}{4} = \frac{6023}{4}

Divide the numbers

p^{5} = \frac{6023}{4}

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

5 p^{5} = 5 \frac{6023}{4}

Calculate

p = 5 \frac{6023}{4}

Solution

More Steps

Evaluate

5 \frac{6023}{4}

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

\frac{5 6023}{5 4}

Multiply by the Conjugate

\frac{5 6023 \times 5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{5 6023 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

56023 \times 258

Multiply the terms

548184 \times 2

Use the commutative property to reorder the terms

2548184

\frac{2 5 48184}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 48184}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 48184}{2}

p = \frac{5 48184}{2}

Alternative Form

p \approx 4.320665

Show Solution