Solve 56-3a^6511 - ScanMath

Question

Simplify the expression

56 - 1533 a^{6}

Evaluate

56 - 3 a^{6} \times 511

Solution

56 - 1533 a^{6}

Show Solution

7 (8 - 219 a^{6})

Evaluate

56 - 3 a^{6} \times 511

Multiply the terms

56 - 1533 a^{6}

Solution

7 (8 - 219 a^{6})

Show Solution

a_{1} = - \frac{6 8 \times 21 9 ^{5}}{219}, a_{2} = \frac{6 8 \times 21 9 ^{5}}{219}

Alternative Form

a_{1} \approx - 0.576025, a_{2} \approx 0.576025

Evaluate

56 - 3 a^{6} \times 511

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

56 - 3 a^{6} \times 511 = 0

Multiply the terms

56 - 1533 a^{6} = 0

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

- 1533 a^{6} = 0 - 56

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

- 1533 a^{6} = - 56

Change the signs on both sides of the equation

1533 a^{6} = 56

Divide both sides

\frac{1533 a ^{6}}{1533} = \frac{56}{1533}

Divide the numbers

a^{6} = \frac{56}{1533}

Cancel out the common factor 7

a^{6} = \frac{8}{219}

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

a = \pm 6 \frac{8}{219}

Simplify the expression

More Steps

Evaluate

6 \frac{8}{219}

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

\frac{6 8}{6 219}

Simplify the radical expression

More Steps

Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{6 219}

Multiply by the Conjugate

\frac{2 \times 6 21 9 ^{5}}{6 219 \times 6 21 9 ^{5}}

Multiply the numbers

More Steps

Evaluate

2 \times 6 21 9^{5}

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

6 2^{3} \times 6 21 9^{5}

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

6 2^{3} \times 21 9^{5}

Calculate the product

6 8 \times 21 9^{5}

\frac{6 8 \times 21 9 ^{5}}{6 219 \times 6 21 9 ^{5}}

Multiply the numbers

More Steps

Evaluate

6219 \times 6 21 9^{5}

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

6 219 \times 21 9^{5}

Calculate the product

6 21 9^{6}

Reduce the index of the radical and exponent with 6

219

\frac{6 8 \times 21 9 ^{5}}{219}

a = \pm \frac{6 8 \times 21 9 ^{5}}{219}

Separate the equation into 2 possible cases

a = \frac{6 8 \times 21 9 ^{5}}{219} a = - \frac{6 8 \times 21 9 ^{5}}{219}

Solution

a_{1} = - \frac{6 8 \times 21 9 ^{5}}{219}, a_{2} = \frac{6 8 \times 21 9 ^{5}}{219}

Alternative Form

a_{1} \approx - 0.576025, a_{2} \approx 0.576025

Show Solution