Solve a^340500 a^340-600

Question

Simplify the expression

1620000 a^{6} - 600

Evaluate

a^{3} \times 40500 a^{3} \times 40 - 600

Solution

More Steps

Evaluate

a^{3} \times 40500 a^{3} \times 40

Multiply the terms with the same base by adding their exponents

a^{3 + 3} \times 40500 \times 40

Add the numbers

a^{6} \times 40500 \times 40

Multiply the terms

a^{6} \times 1620000

Use the commutative property to reorder the terms

1620000 a^{6}

1620000 a^{6} - 600

Show Solution

Factor the expression

600 (2700 a^{6} - 1)

Evaluate

a^{3} \times 40500 a^{3} \times 40 - 600

Multiply

More Steps

Evaluate

a^{3} \times 40500 a^{3} \times 40

Multiply the terms with the same base by adding their exponents

a^{3 + 3} \times 40500 \times 40

Add the numbers

a^{6} \times 40500 \times 40

Multiply the terms

a^{6} \times 1620000

Use the commutative property to reorder the terms

1620000 a^{6}

1620000 a^{6} - 600

Solution

600 (2700 a^{6} - 1)

Show Solution

Find the roots

a_{1} = - \frac{6 270 0 ^{5}}{2700}, a_{2} = \frac{6 270 0 ^{5}}{2700}

Alternative Form

a_{1} \approx - 0.267982, a_{2} \approx 0.267982

Evaluate

a^{3} \times 40500 a^{3} \times 40 - 600

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

a^{3} \times 40500 a^{3} \times 40 - 600 = 0

Multiply

More Steps

Multiply the terms

a^{3} \times 40500 a^{3} \times 40

Multiply the terms with the same base by adding their exponents

a^{3 + 3} \times 40500 \times 40

Add the numbers

a^{6} \times 40500 \times 40

Multiply the terms

a^{6} \times 1620000

Use the commutative property to reorder the terms

1620000 a^{6}

1620000 a^{6} - 600 = 0

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

1620000 a^{6} = 0 + 600

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

1620000 a^{6} = 600

Divide both sides

\frac{1620000 a ^{6}}{1620000} = \frac{600}{1620000}

Divide the numbers

a^{6} = \frac{600}{1620000}

Cancel out the common factor 600

a^{6} = \frac{1}{2700}

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

a = \pm 6 \frac{1}{2700}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{2700}

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

\frac{6 1}{6 2700}

Simplify the radical expression

\frac{1}{6 2700}

Multiply by the Conjugate

\frac{6 270 0 ^{5}}{6 2700 \times 6 270 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

62700 \times 6 270 0^{5}

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

6 2700 \times 270 0^{5}

Calculate the product

6 270 0^{6}

Reduce the index of the radical and exponent with 6

2700

\frac{6 270 0 ^{5}}{2700}

a = \pm \frac{6 270 0 ^{5}}{2700}

Separate the equation into 2 possible cases

a = \frac{6 270 0 ^{5}}{2700} a = - \frac{6 270 0 ^{5}}{2700}

Solution

a_{1} = - \frac{6 270 0 ^{5}}{2700}, a_{2} = \frac{6 270 0 ^{5}}{2700}

Alternative Form

a_{1} \approx - 0.267982, a_{2} \approx 0.267982

Show Solution