Solve (6n^3n)-7 - ScanMath

Question

Simplify the expression

6 n^{4} - 7

Evaluate

(6 n^{3} \times n) - 7

Solution

More Steps

Evaluate

6 n^{3} \times n

Multiply the terms with the same base by adding their exponents

6 n^{3 + 1}

Add the numbers

6 n^{4}

6 n^{4} - 7

Show Solution

n_{1} = - \frac{4 1512}{6}, n_{2} = \frac{4 1512}{6}

Alternative Form

n_{1} \approx - 1.03929, n_{2} \approx 1.03929

Evaluate

(6 n^{3} \times n) - 7

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

(6 n^{3} \times n) - 7 = 0

Multiply

More Steps

Multiply the terms

6 n^{3} \times n

Multiply the terms with the same base by adding their exponents

6 n^{3 + 1}

Add the numbers

6 n^{4}

6 n^{4} - 7 = 0

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

6 n^{4} = 0 + 7

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

6 n^{4} = 7

Divide both sides

\frac{6 n ^{4}}{6} = \frac{7}{6}

Divide the numbers

n^{4} = \frac{7}{6}

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

n = \pm 4 \frac{7}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{6}

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

\frac{4 7}{4 6}

Multiply by the Conjugate

\frac{4 7 \times 4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 7 \times 4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4216

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

4 7 \times 216

Calculate the product

41512

\frac{4 1512}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4 6^{3}

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

4 6 \times 6^{3}

Calculate the product

4 6^{4}

Reduce the index of the radical and exponent with 4

6

\frac{4 1512}{6}

n = \pm \frac{4 1512}{6}

Separate the equation into 2 possible cases

n = \frac{4 1512}{6} n = - \frac{4 1512}{6}

Solution

n_{1} = - \frac{4 1512}{6}, n_{2} = \frac{4 1512}{6}

Alternative Form

n_{1} \approx - 1.03929, n_{2} \approx 1.03929

Show Solution