Solve 500-1576 a^6

Question

Factor the expression

4 (125 - 394 a^{6})

Evaluate

500 - 1576 a^{6}

Solution

4 (125 - 394 a^{6})

Show Solution

a_{1} = - \frac{6 125 \times 39 4 ^{5}}{394}, a_{2} = \frac{6 125 \times 39 4 ^{5}}{394}

Alternative Form

a_{1} \approx - 0.825852, a_{2} \approx 0.825852

Evaluate

500 - 1576 a^{6}

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

500 - 1576 a^{6} = 0

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

- 1576 a^{6} = 0 - 500

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

- 1576 a^{6} = - 500

Change the signs on both sides of the equation

1576 a^{6} = 500

Divide both sides

\frac{1576 a ^{6}}{1576} = \frac{500}{1576}

Divide the numbers

a^{6} = \frac{500}{1576}

Cancel out the common factor 4

a^{6} = \frac{125}{394}

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

a = \pm 6 \frac{125}{394}

Simplify the expression

More Steps

Evaluate

6 \frac{125}{394}

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

\frac{6 125}{6 394}

Simplify the radical expression

More Steps

Evaluate

6125

Write the number in exponential form with the base of 5

6 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{5}{6 394}

Multiply by the Conjugate

\frac{5 \times 6 39 4 ^{5}}{6 394 \times 6 39 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

5 \times 6 39 4^{5}

Use n a = mn a^{m} to expand the expression

6 5^{3} \times 6 39 4^{5}

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

6 5^{3} \times 39 4^{5}

Calculate the product

6 125 \times 39 4^{5}

\frac{6 125 \times 39 4 ^{5}}{6 394 \times 6 39 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

6394 \times 6 39 4^{5}

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

6 394 \times 39 4^{5}

Calculate the product

6 39 4^{6}

Reduce the index of the radical and exponent with 6

394

\frac{6 125 \times 39 4 ^{5}}{394}

a = \pm \frac{6 125 \times 39 4 ^{5}}{394}

Separate the equation into 2 possible cases

a = \frac{6 125 \times 39 4 ^{5}}{394} a = - \frac{6 125 \times 39 4 ^{5}}{394}

Solution

a_{1} = - \frac{6 125 \times 39 4 ^{5}}{394}, a_{2} = \frac{6 125 \times 39 4 ^{5}}{394}

Alternative Form

a_{1} \approx - 0.825852, a_{2} \approx 0.825852

Show Solution