Solve a^68-8272/2020

Question

Simplify the expression

8 a^{6} - \frac{2068}{505}

Evaluate

a^{6} \times 8 - \frac{8272}{2020}

Cancel out the common factor 4

a^{6} \times 8 - \frac{2068}{505}

Solution

8 a^{6} - \frac{2068}{505}

Show Solution

\frac{4}{505} (1010 a^{6} - 517)

Evaluate

a^{6} \times 8 - \frac{8272}{2020}

Cancel out the common factor 4

a^{6} \times 8 - \frac{2068}{505}

Use the commutative property to reorder the terms

8 a^{6} - \frac{2068}{505}

Solution

\frac{4}{505} (1010 a^{6} - 517)

Show Solution

a_{1} = - \frac{6 517 \times 101 0 ^{5}}{1010}, a_{2} = \frac{6 517 \times 101 0 ^{5}}{1010}

Alternative Form

a_{1} \approx - 0.894393, a_{2} \approx 0.894393

Evaluate

a^{6} \times 8 - \frac{8272}{2020}

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

a^{6} \times 8 - \frac{8272}{2020} = 0

Cancel out the common factor 4

a^{6} \times 8 - \frac{2068}{505} = 0

Use the commutative property to reorder the terms

8 a^{6} - \frac{2068}{505} = 0

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

8 a^{6} = 0 + \frac{2068}{505}

Add the terms

8 a^{6} = \frac{2068}{505}

Multiply by the reciprocal

8 a^{6} \times \frac{1}{8} = \frac{2068}{505} \times \frac{1}{8}

Multiply

a^{6} = \frac{2068}{505} \times \frac{1}{8}

Multiply

More Steps

Evaluate

\frac{2068}{505} \times \frac{1}{8}

Reduce the numbers

\frac{517}{505} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{517}{505 \times 2}

Multiply the numbers

\frac{517}{1010}

a^{6} = \frac{517}{1010}

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

a = \pm 6 \frac{517}{1010}

Simplify the expression

More Steps

Evaluate

6 \frac{517}{1010}

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

\frac{6 517}{6 1010}

Multiply by the Conjugate

\frac{6 517 \times 6 101 0 ^{5}}{6 1010 \times 6 101 0 ^{5}}

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

\frac{6 517 \times 101 0 ^{5}}{6 1010 \times 6 101 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

61010 \times 6 101 0^{5}

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

6 1010 \times 101 0^{5}

Calculate the product

6 101 0^{6}

Reduce the index of the radical and exponent with 6

1010

\frac{6 517 \times 101 0 ^{5}}{1010}

a = \pm \frac{6 517 \times 101 0 ^{5}}{1010}

Separate the equation into 2 possible cases

a = \frac{6 517 \times 101 0 ^{5}}{1010} a = - \frac{6 517 \times 101 0 ^{5}}{1010}

Solution

a_{1} = - \frac{6 517 \times 101 0 ^{5}}{1010}, a_{2} = \frac{6 517 \times 101 0 ^{5}}{1010}

Alternative Form

a_{1} \approx - 0.894393, a_{2} \approx 0.894393

Show Solution