Solve 1011a^614-201

Question

Simplify the expression

14154 a^{6} - 201

Evaluate

1011 a^{6} \times 14 - 201

Solution

14154 a^{6} - 201

Show Solution

3 (4718 a^{6} - 67)

Evaluate

1011 a^{6} \times 14 - 201

Multiply the terms

14154 a^{6} - 201

Solution

3 (4718 a^{6} - 67)

Show Solution

a_{1} = - \frac{6 67 \times 471 8 ^{5}}{4718}, a_{2} = \frac{6 67 \times 471 8 ^{5}}{4718}

Alternative Form

a_{1} \approx - 0.492099, a_{2} \approx 0.492099

Evaluate

1011 a^{6} \times 14 - 201

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

1011 a^{6} \times 14 - 201 = 0

Multiply the terms

14154 a^{6} - 201 = 0

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

14154 a^{6} = 0 + 201

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

14154 a^{6} = 201

Divide both sides

\frac{14154 a ^{6}}{14154} = \frac{201}{14154}

Divide the numbers

a^{6} = \frac{201}{14154}

Cancel out the common factor 3

a^{6} = \frac{67}{4718}

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

a = \pm 6 \frac{67}{4718}

Simplify the expression

More Steps

Evaluate

6 \frac{67}{4718}

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

\frac{6 67}{6 4718}

Multiply by the Conjugate

\frac{6 67 \times 6 471 8 ^{5}}{6 4718 \times 6 471 8 ^{5}}

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

\frac{6 67 \times 471 8 ^{5}}{6 4718 \times 6 471 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

64718 \times 6 471 8^{5}

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

6 4718 \times 471 8^{5}

Calculate the product

6 471 8^{6}

Reduce the index of the radical and exponent with 6

4718

\frac{6 67 \times 471 8 ^{5}}{4718}

a = \pm \frac{6 67 \times 471 8 ^{5}}{4718}

Separate the equation into 2 possible cases

a = \frac{6 67 \times 471 8 ^{5}}{4718} a = - \frac{6 67 \times 471 8 ^{5}}{4718}

Solution

a_{1} = - \frac{6 67 \times 471 8 ^{5}}{4718}, a_{2} = \frac{6 67 \times 471 8 ^{5}}{4718}

Alternative Form

a_{1} \approx - 0.492099, a_{2} \approx 0.492099

Show Solution