Solve F^250 F^3502023-2024

Question

Simplify the expression

25101150 F^{5} - 2024

Evaluate

F^{2} \times 50 F^{3} \times 502023 - 2024

Solution

More Steps

Evaluate

F^{2} \times 50 F^{3} \times 502023

Multiply the terms with the same base by adding their exponents

F^{2 + 3} \times 50 \times 502023

Add the numbers

F^{5} \times 50 \times 502023

Multiply the terms

F^{5} \times 25101150

Use the commutative property to reorder the terms

25101150 F^{5}

25101150 F^{5} - 2024

Show Solution

Factor the expression

2 (12550575 F^{5} - 1012)

Evaluate

F^{2} \times 50 F^{3} \times 502023 - 2024

Multiply

More Steps

Evaluate

F^{2} \times 50 F^{3} \times 502023

Multiply the terms with the same base by adding their exponents

F^{2 + 3} \times 50 \times 502023

Add the numbers

F^{5} \times 50 \times 502023

Multiply the terms

F^{5} \times 25101150

Use the commutative property to reorder the terms

25101150 F^{5}

25101150 F^{5} - 2024

Solution

2 (12550575 F^{5} - 1012)

Show Solution

Find the roots

F = \frac{5 1012 \times 1255057 5 ^{4}}{12550575}

Alternative Form

F \approx 0.151811

Evaluate

F^{2} \times 50 F^{3} \times 502023 - 2024

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

F^{2} \times 50 F^{3} \times 502023 - 2024 = 0

Multiply

More Steps

Multiply the terms

F^{2} \times 50 F^{3} \times 502023

Multiply the terms with the same base by adding their exponents

F^{2 + 3} \times 50 \times 502023

Add the numbers

F^{5} \times 50 \times 502023

Multiply the terms

F^{5} \times 25101150

Use the commutative property to reorder the terms

25101150 F^{5}

25101150 F^{5} - 2024 = 0

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

25101150 F^{5} = 0 + 2024

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

25101150 F^{5} = 2024

Divide both sides

\frac{25101150 F ^{5}}{25101150} = \frac{2024}{25101150}

Divide the numbers

F^{5} = \frac{2024}{25101150}

Cancel out the common factor 2

F^{5} = \frac{1012}{12550575}

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

5 F^{5} = 5 \frac{1012}{12550575}

Calculate

F = 5 \frac{1012}{12550575}

Solution

More Steps

Evaluate

5 \frac{1012}{12550575}

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

\frac{5 1012}{5 12550575}

Multiply by the Conjugate

\frac{5 1012 \times 5 1255057 5 ^{4}}{5 12550575 \times 5 1255057 5 ^{4}}

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

\frac{5 1012 \times 1255057 5 ^{4}}{5 12550575 \times 5 1255057 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

512550575 \times 5 1255057 5^{4}

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

5 12550575 \times 1255057 5^{4}

Calculate the product

5 1255057 5^{5}

Reduce the index of the radical and exponent with 5

12550575

\frac{5 1012 \times 1255057 5 ^{4}}{12550575}

F = \frac{5 1012 \times 1255057 5 ^{4}}{12550575}

Alternative Form

F \approx 0.151811

Show Solution