Solve a^642-200-10-70

Question

Simplify the expression

42 a^{6} - 280

Evaluate

a^{6} \times 42 - 200 - 10 - 70

Use the commutative property to reorder the terms

42 a^{6} - 200 - 10 - 70

Solution

42 a^{6} - 280

Show Solution

14 (3 a^{6} - 20)

Evaluate

a^{6} \times 42 - 200 - 10 - 70

Use the commutative property to reorder the terms

42 a^{6} - 200 - 10 - 70

Subtract the numbers

42 a^{6} - 210 - 70

Subtract the numbers

42 a^{6} - 280

Solution

14 (3 a^{6} - 20)

Show Solution

a_{1} = - \frac{6 4860}{3}, a_{2} = \frac{6 4860}{3}

Alternative Form

a_{1} \approx - 1.371886, a_{2} \approx 1.371886

Evaluate

a^{6} \times 42 - 200 - 10 - 70

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

a^{6} \times 42 - 200 - 10 - 70 = 0

Use the commutative property to reorder the terms

42 a^{6} - 200 - 10 - 70 = 0

Subtract the numbers

42 a^{6} - 210 - 70 = 0

Subtract the numbers

42 a^{6} - 280 = 0

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

42 a^{6} = 0 + 280

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

42 a^{6} = 280

Divide both sides

\frac{42 a ^{6}}{42} = \frac{280}{42}

Divide the numbers

a^{6} = \frac{280}{42}

Cancel out the common factor 14

a^{6} = \frac{20}{3}

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

a = \pm 6 \frac{20}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{20}{3}

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

\frac{6 20}{6 3}

Multiply by the Conjugate

\frac{6 20 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 20 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

620 \times 6243

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

6 20 \times 243

Calculate the product

64860

\frac{6 4860}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{6 4860}{3}

a = \pm \frac{6 4860}{3}

Separate the equation into 2 possible cases

a = \frac{6 4860}{3} a = - \frac{6 4860}{3}

Solution

a_{1} = - \frac{6 4860}{3}, a_{2} = \frac{6 4860}{3}

Alternative Form

a_{1} \approx - 1.371886, a_{2} \approx 1.371886

Show Solution