Solve n*n^33 = 7 - ScanMath

Question

n \times n^{3} \times 3 = 7

Solve the equation

n_{1} = - \frac{4 189}{3}, n_{2} = \frac{4 189}{3}

Alternative Form

n_{1} \approx - 1.235931, n_{2} \approx 1.235931

Evaluate

n \times n^{3} \times 3 = 7

Multiply

More Steps

Evaluate

n \times n^{3} \times 3

Multiply the terms with the same base by adding their exponents

n^{1 + 3} \times 3

Add the numbers

n^{4} \times 3

Use the commutative property to reorder the terms

3 n^{4}

3 n^{4} = 7

Divide both sides

\frac{3 n ^{4}}{3} = \frac{7}{3}

Divide the numbers

n^{4} = \frac{7}{3}

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

n = \pm 4 \frac{7}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{3}

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

\frac{4 7}{4 3}

Multiply by the Conjugate

\frac{4 7 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 7 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 427

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

4 7 \times 27

Calculate the product

4189

\frac{4 189}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 189}{3}

n = \pm \frac{4 189}{3}

Separate the equation into 2 possible cases

n = \frac{4 189}{3} n = - \frac{4 189}{3}

Solution

n_{1} = - \frac{4 189}{3}, n_{2} = \frac{4 189}{3}

Alternative Form

n_{1} \approx - 1.235931, n_{2} \approx 1.235931

Show Solution