Solve 8l1*500l^413-433

Question

Simplify the expression

52000 l^{5} - 433

Evaluate

8 l \times 1 \times 500 l^{4} \times 13 - 433

Solution

More Steps

Evaluate

8 l \times 1 \times 500 l^{4} \times 13

Rewrite the expression

8 l \times 500 l^{4} \times 13

Multiply the terms

More Steps

Evaluate

8 \times 500 \times 13

Multiply the terms

4000 \times 13

Multiply the numbers

52000

52000 l \times l^{4}

Multiply the terms with the same base by adding their exponents

52000 l^{1 + 4}

Add the numbers

52000 l^{5}

52000 l^{5} - 433

Show Solution

Find the roots

l = \frac{5 433 \times 162 5 ^{4}}{3250}

Alternative Form

l \approx 0.383793

Evaluate

8 l \times 1 \times 500 l^{4} \times 13 - 433

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

8 l \times 1 \times 500 l^{4} \times 13 - 433 = 0

Multiply the terms

More Steps

Multiply the terms

8 l \times 1 \times 500 l^{4} \times 13

Rewrite the expression

8 l \times 500 l^{4} \times 13

Multiply the terms

More Steps

Evaluate

8 \times 500 \times 13

Multiply the terms

4000 \times 13

Multiply the numbers

52000

52000 l \times l^{4}

Multiply the terms with the same base by adding their exponents

52000 l^{1 + 4}

Add the numbers

52000 l^{5}

52000 l^{5} - 433 = 0

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

52000 l^{5} = 0 + 433

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

52000 l^{5} = 433

Divide both sides

\frac{52000 l ^{5}}{52000} = \frac{433}{52000}

Divide the numbers

l^{5} = \frac{433}{52000}

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

5 l^{5} = 5 \frac{433}{52000}

Calculate

l = 5 \frac{433}{52000}

Solution

More Steps

Evaluate

5 \frac{433}{52000}

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

\frac{5 433}{5 52000}

Simplify the radical expression

More Steps

Evaluate

552000

Write the expression as a product where the root of one of the factors can be evaluated

5 32 \times 1625

Write the number in exponential form with the base of 2

5 2^{5} \times 1625

The root of a product is equal to the product of the roots of each factor

5 2^{5} \times 51625

Reduce the index of the radical and exponent with 5

251625

\frac{5 433}{2 5 1625}

Multiply by the Conjugate

\frac{5 433 \times 5 162 5 ^{4}}{2 5 1625 \times 5 162 5 ^{4}}

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

\frac{5 433 \times 162 5 ^{4}}{2 5 1625 \times 5 162 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

251625 \times 5 162 5^{4}

Multiply the terms

2 \times 1625

Multiply the terms

3250

\frac{5 433 \times 162 5 ^{4}}{3250}

l = \frac{5 433 \times 162 5 ^{4}}{3250}

Alternative Form

l \approx 0.383793

Show Solution