Solve 330-2606:r^51

Question

Simplify the expression

\frac{330 r ^{5} - 2606}{r ^{5}}

Evaluate

330 - 2606 \div (r^{5} \times 1)

Any expression multiplied by 1 remains the same

330 - 2606 \div r^{5}

Rewrite the expression

330 - \frac{2606}{r ^{5}}

Reduce fractions to a common denominator

\frac{330 r ^{5}}{r ^{5}} - \frac{2606}{r ^{5}}

Solution

\frac{330 r ^{5} - 2606}{r ^{5}}

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Find the excluded values

r = 0

Evaluate

330 - 2606 \div (r^{5} \times 1)

To find the excluded values,set the denominators equal to 0

r^{5} \times 1 = 0

Any expression multiplied by 1 remains the same

r^{5} = 0

Solution

r = 0

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Find the roots

r = \frac{5 1303 \times 16 5 ^{4}}{165}

Alternative Form

r \approx 1.511792

Evaluate

330 - 2606 \div (r^{5} \times 1)

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

330 - 2606 \div (r^{5} \times 1) = 0

Find the domain

More Steps

Evaluate

r^{5} \times 1 \neq = 0

Any expression multiplied by 1 remains the same

r^{5} \neq = 0

The only way a power can not be 0 is when the base not equals 0

r \neq = 0

330 - 2606 \div (r^{5} \times 1) = 0, r \neq = 0

Calculate

330 - 2606 \div (r^{5} \times 1) = 0

Any expression multiplied by 1 remains the same

330 - 2606 \div r^{5} = 0

Rewrite the expression

330 - \frac{2606}{r ^{5}} = 0

Subtract the terms

More Steps

Simplify

330 - \frac{2606}{r ^{5}}

Reduce fractions to a common denominator

\frac{330 r ^{5}}{r ^{5}} - \frac{2606}{r ^{5}}

Write all numerators above the common denominator

\frac{330 r ^{5} - 2606}{r ^{5}}

\frac{330 r ^{5} - 2606}{r ^{5}} = 0

Cross multiply

330 r^{5} - 2606 = r^{5} \times 0

Simplify the equation

330 r^{5} - 2606 = 0

Move the constant to the right side

330 r^{5} = 2606

Divide both sides

\frac{330 r ^{5}}{330} = \frac{2606}{330}

Divide the numbers

r^{5} = \frac{2606}{330}

Cancel out the common factor 2

r^{5} = \frac{1303}{165}

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

5 r^{5} = 5 \frac{1303}{165}

Calculate

r = 5 \frac{1303}{165}

Simplify the root

More Steps

Evaluate

5 \frac{1303}{165}

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

\frac{5 1303}{5 165}

Multiply by the Conjugate

\frac{5 1303 \times 5 16 5 ^{4}}{5 165 \times 5 16 5 ^{4}}

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

\frac{5 1303 \times 16 5 ^{4}}{5 165 \times 5 16 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

5165 \times 5 16 5^{4}

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

5 165 \times 16 5^{4}

Calculate the product

5 16 5^{5}

Reduce the index of the radical and exponent with 5

165

\frac{5 1303 \times 16 5 ^{4}}{165}

r = \frac{5 1303 \times 16 5 ^{4}}{165}

Check if the solution is in the defined range

r = \frac{5 1303 \times 16 5 ^{4}}{165}, r \neq = 0

Solution

r = \frac{5 1303 \times 16 5 ^{4}}{165}

Alternative Form

r \approx 1.511792

Show Solution