Solve n^6450-60001

Question

Simplify the expression

450 n^{6} - 60001

Evaluate

n^{6} \times 450 - 60001

Solution

450 n^{6} - 60001

Show Solution

n_{1} = - \frac{6 60001 \times 45 0 ^{5}}{450}, n_{2} = \frac{6 60001 \times 45 0 ^{5}}{450}

Alternative Form

n_{1} \approx - 2.260256, n_{2} \approx 2.260256

Evaluate

n^{6} \times 450 - 60001

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

n^{6} \times 450 - 60001 = 0

Use the commutative property to reorder the terms

450 n^{6} - 60001 = 0

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

450 n^{6} = 0 + 60001

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

450 n^{6} = 60001

Divide both sides

\frac{450 n ^{6}}{450} = \frac{60001}{450}

Divide the numbers

n^{6} = \frac{60001}{450}

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

n = \pm 6 \frac{60001}{450}

Simplify the expression

More Steps

Evaluate

6 \frac{60001}{450}

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

\frac{6 60001}{6 450}

Multiply by the Conjugate

\frac{6 60001 \times 6 45 0 ^{5}}{6 450 \times 6 45 0 ^{5}}

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

\frac{6 60001 \times 45 0 ^{5}}{6 450 \times 6 45 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

6450 \times 6 45 0^{5}

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

6 450 \times 45 0^{5}

Calculate the product

6 45 0^{6}

Reduce the index of the radical and exponent with 6

450

\frac{6 60001 \times 45 0 ^{5}}{450}

n = \pm \frac{6 60001 \times 45 0 ^{5}}{450}

Separate the equation into 2 possible cases

n = \frac{6 60001 \times 45 0 ^{5}}{450} n = - \frac{6 60001 \times 45 0 ^{5}}{450}

Solution

n_{1} = - \frac{6 60001 \times 45 0 ^{5}}{450}, n_{2} = \frac{6 60001 \times 45 0 ^{5}}{450}

Alternative Form

n_{1} \approx - 2.260256, n_{2} \approx 2.260256

Show Solution