Solve 16J^614-1 - ScanMath

Question

Simplify the expression

224 J^{6} - 1

Evaluate

16 J^{6} \times 14 - 1

Solution

224 J^{6} - 1

Show Solution

J_{1} = - \frac{6 22 4 ^{5}}{224}, J_{2} = \frac{6 22 4 ^{5}}{224}

Alternative Form

J_{1} \approx - 0.405781, J_{2} \approx 0.405781

Evaluate

16 J^{6} \times 14 - 1

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

16 J^{6} \times 14 - 1 = 0

Multiply the terms

224 J^{6} - 1 = 0

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

224 J^{6} = 0 + 1

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

224 J^{6} = 1

Divide both sides

\frac{224 J ^{6}}{224} = \frac{1}{224}

Divide the numbers

J^{6} = \frac{1}{224}

Take the root of both sides of the equation and remember to use both positive and negative roots

J = \pm 6 \frac{1}{224}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{224}

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

\frac{6 1}{6 224}

Simplify the radical expression

\frac{1}{6 224}

Multiply by the Conjugate

\frac{6 22 4 ^{5}}{6 224 \times 6 22 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

6224 \times 6 22 4^{5}

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

6 224 \times 22 4^{5}

Calculate the product

6 22 4^{6}

Reduce the index of the radical and exponent with 6

224

\frac{6 22 4 ^{5}}{224}

J = \pm \frac{6 22 4 ^{5}}{224}

Separate the equation into 2 possible cases

J = \frac{6 22 4 ^{5}}{224} J = - \frac{6 22 4 ^{5}}{224}

Solution

J_{1} = - \frac{6 22 4 ^{5}}{224}, J_{2} = \frac{6 22 4 ^{5}}{224}

Alternative Form

J_{1} \approx - 0.405781, J_{2} \approx 0.405781

Show Solution