Solve 8=4v^535v - ScanMath

Question

Solve the equation

v_{1} = - \frac{6 2 \times 3 5 ^{5}}{35}, v_{2} = \frac{6 2 \times 3 5 ^{5}}{35}

Alternative Form

v_{1} \approx - 0.620622, v_{2} \approx 0.620622

Evaluate

8 = 4 v^{5} \times 35 v

Multiply

More Steps

Evaluate

4 v^{5} \times 35 v

Multiply the terms

140 v^{5} \times v

Multiply the terms with the same base by adding their exponents

140 v^{5 + 1}

Add the numbers

140 v^{6}

8 = 140 v^{6}

Swap the sides of the equation

140 v^{6} = 8

Divide both sides

\frac{140 v ^{6}}{140} = \frac{8}{140}

Divide the numbers

v^{6} = \frac{8}{140}

Cancel out the common factor 4

v^{6} = \frac{2}{35}

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

v = \pm 6 \frac{2}{35}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{35}

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

\frac{6 2}{6 35}

Multiply by the Conjugate

\frac{6 2 \times 6 3 5 ^{5}}{6 35 \times 6 3 5 ^{5}}

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

\frac{6 2 \times 3 5 ^{5}}{6 35 \times 6 3 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

635 \times 6 3 5^{5}

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

6 35 \times 3 5^{5}

Calculate the product

6 3 5^{6}

Reduce the index of the radical and exponent with 6

35

\frac{6 2 \times 3 5 ^{5}}{35}

v = \pm \frac{6 2 \times 3 5 ^{5}}{35}

Separate the equation into 2 possible cases

v = \frac{6 2 \times 3 5 ^{5}}{35} v = - \frac{6 2 \times 3 5 ^{5}}{35}

Solution

v_{1} = - \frac{6 2 \times 3 5 ^{5}}{35}, v_{2} = \frac{6 2 \times 3 5 ^{5}}{35}

Alternative Form

v_{1} \approx - 0.620622, v_{2} \approx 0.620622

Show Solution