Solve 1a^6002395-31

Question

Simplify the expression

2395 a^{6} - 31

Evaluate

1 \times a^{6} \times 2395 - 31

Solution

More Steps

Evaluate

1 \times a^{6} \times 2395

Rewrite the expression

a^{6} \times 2395

Use the commutative property to reorder the terms

2395 a^{6}

2395 a^{6} - 31

Show Solution

a_{1} = - \frac{6 31 \times 239 5 ^{5}}{2395}, a_{2} = \frac{6 31 \times 239 5 ^{5}}{2395}

Alternative Form

a_{1} \approx - 0.484555, a_{2} \approx 0.484555

Evaluate

1 \times a^{6} \times 2395 - 31

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

1 \times a^{6} \times 2395 - 31 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times a^{6} \times 2395

Rewrite the expression

a^{6} \times 2395

Use the commutative property to reorder the terms

2395 a^{6}

2395 a^{6} - 31 = 0

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

2395 a^{6} = 0 + 31

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

2395 a^{6} = 31

Divide both sides

\frac{2395 a ^{6}}{2395} = \frac{31}{2395}

Divide the numbers

a^{6} = \frac{31}{2395}

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

a = \pm 6 \frac{31}{2395}

Simplify the expression

More Steps

Evaluate

6 \frac{31}{2395}

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

\frac{6 31}{6 2395}

Multiply by the Conjugate

\frac{6 31 \times 6 239 5 ^{5}}{6 2395 \times 6 239 5 ^{5}}

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

\frac{6 31 \times 239 5 ^{5}}{6 2395 \times 6 239 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

62395 \times 6 239 5^{5}

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

6 2395 \times 239 5^{5}

Calculate the product

6 239 5^{6}

Reduce the index of the radical and exponent with 6

2395

\frac{6 31 \times 239 5 ^{5}}{2395}

a = \pm \frac{6 31 \times 239 5 ^{5}}{2395}

Separate the equation into 2 possible cases

a = \frac{6 31 \times 239 5 ^{5}}{2395} a = - \frac{6 31 \times 239 5 ^{5}}{2395}

Solution

a_{1} = - \frac{6 31 \times 239 5 ^{5}}{2395}, a_{2} = \frac{6 31 \times 239 5 ^{5}}{2395}

Alternative Form

a_{1} \approx - 0.484555, a_{2} \approx 0.484555

Show Solution