Solve 4v^373v=9 - ScanMath

Question

Solve the equation

v_{1} = - \frac{4 9 \times 29 2 ^{3}}{292}, v_{2} = \frac{4 9 \times 29 2 ^{3}}{292}

Alternative Form

v_{1} \approx - 0.419001, v_{2} \approx 0.419001

Evaluate

4 v^{3} \times 73 v = 9

Multiply

More Steps

Evaluate

4 v^{3} \times 73 v

Multiply the terms

292 v^{3} \times v

Multiply the terms with the same base by adding their exponents

292 v^{3 + 1}

Add the numbers

292 v^{4}

292 v^{4} = 9

Divide both sides

\frac{292 v ^{4}}{292} = \frac{9}{292}

Divide the numbers

v^{4} = \frac{9}{292}

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

v = \pm 4 \frac{9}{292}

Simplify the expression

More Steps

Evaluate

4 \frac{9}{292}

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

\frac{4 9}{4 292}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{4 292}

Multiply by the Conjugate

\frac{3 \times 4 29 2 ^{3}}{4 292 \times 4 29 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

3 \times 4 29 2^{3}

Use n a = mn a^{m} to expand the expression

4 3^{2} \times 4 29 2^{3}

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

4 3^{2} \times 29 2^{3}

Calculate the product

4 9 \times 29 2^{3}

\frac{4 9 \times 29 2 ^{3}}{4 292 \times 4 29 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

4292 \times 4 29 2^{3}

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

4 292 \times 29 2^{3}

Calculate the product

4 29 2^{4}

Reduce the index of the radical and exponent with 4

292

\frac{4 9 \times 29 2 ^{3}}{292}

v = \pm \frac{4 9 \times 29 2 ^{3}}{292}

Separate the equation into 2 possible cases

v = \frac{4 9 \times 29 2 ^{3}}{292} v = - \frac{4 9 \times 29 2 ^{3}}{292}

Solution

v_{1} = - \frac{4 9 \times 29 2 ^{3}}{292}, v_{2} = \frac{4 9 \times 29 2 ^{3}}{292}

Alternative Form

v_{1} \approx - 0.419001, v_{2} \approx 0.419001

Show Solution