Solve Q/Q^601-96 - ScanMath

Question

Simplify the expression

\frac{1 - 96 Q ^{5}}{Q ^{5}}

Evaluate

\frac{Q}{Q ^{6}} \times 1 - 96

Divide the terms

More Steps

Evaluate

\frac{Q}{Q ^{6}}

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

\frac{1}{Q ^{6 - 1}}

Reduce the fraction

\frac{1}{Q ^{5}}

\frac{1}{Q ^{5}} \times 1 - 96

Calculate

\frac{1}{Q ^{5}} - 96

Reduce fractions to a common denominator

\frac{1}{Q ^{5}} - \frac{96 Q ^{5}}{Q ^{5}}

Solution

\frac{1 - 96 Q ^{5}}{Q ^{5}}

Show Solution

Find the excluded values

Q = 0

Evaluate

\frac{Q}{Q ^{6}} \times 1 - 96

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

Q^{6} = 0

Solution

Q = 0

Show Solution

Find the roots

Q = \frac{5 81}{6}

Alternative Form

Q \approx 0.401371

Evaluate

\frac{Q}{Q ^{6}} \times 1 - 96

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

\frac{Q}{Q ^{6}} \times 1 - 96 = 0

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

\frac{Q}{Q ^{6}} \times 1 - 96 = 0, Q \neq = 0

Calculate

\frac{Q}{Q ^{6}} \times 1 - 96 = 0

Divide the terms

More Steps

Evaluate

\frac{Q}{Q ^{6}}

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

\frac{1}{Q ^{6 - 1}}

Reduce the fraction

\frac{1}{Q ^{5}}

\frac{1}{Q ^{5}} \times 1 - 96 = 0

Calculate

\frac{1}{Q ^{5}} - 96 = 0

Subtract the terms

More Steps

Simplify

\frac{1}{Q ^{5}} - 96

Reduce fractions to a common denominator

\frac{1}{Q ^{5}} - \frac{96 Q ^{5}}{Q ^{5}}

Write all numerators above the common denominator

\frac{1 - 96 Q ^{5}}{Q ^{5}}

\frac{1 - 96 Q ^{5}}{Q ^{5}} = 0

Cross multiply

1 - 96 Q^{5} = Q^{5} \times 0

Simplify the equation

1 - 96 Q^{5} = 0

Rewrite the expression

- 96 Q^{5} = - 1

Change the signs on both sides of the equation

96 Q^{5} = 1

Divide both sides

\frac{96 Q ^{5}}{96} = \frac{1}{96}

Divide the numbers

Q^{5} = \frac{1}{96}

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

5 Q^{5} = 5 \frac{1}{96}

Calculate

Q = 5 \frac{1}{96}

Simplify the root

More Steps

Evaluate

5 \frac{1}{96}

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

\frac{5 1}{5 96}

Simplify the radical expression

\frac{1}{5 96}

Simplify the radical expression

More Steps

Evaluate

596

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

5 32 \times 3

Write the number in exponential form with the base of 2

5 2^{5} \times 3

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

5 2^{5} \times 53

Reduce the index of the radical and exponent with 5

253

\frac{1}{2 5 3}

Multiply by the Conjugate

\frac{5 3 ^{4}}{2 5 3 \times 5 3 ^{4}}

Simplify

\frac{5 81}{2 5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

253 \times 5 3^{4}

Multiply the terms

2 \times 3

Multiply the terms

6

\frac{5 81}{6}

Q = \frac{5 81}{6}

Check if the solution is in the defined range

Q = \frac{5 81}{6}, Q \neq = 0

Solution

Q = \frac{5 81}{6}

Alternative Form

Q \approx 0.401371

Show Solution