Solve 7=6w^343w - ScanMath

Question

Solve the equation

w_{1} = - \frac{4 7 \times 25 8 ^{3}}{258}, w_{2} = \frac{4 7 \times 25 8 ^{3}}{258}

Alternative Form

w_{1} \approx - 0.405854, w_{2} \approx 0.405854

Evaluate

7 = 6 w^{3} \times 43 w

Multiply

More Steps

Evaluate

6 w^{3} \times 43 w

Multiply the terms

258 w^{3} \times w

Multiply the terms with the same base by adding their exponents

258 w^{3 + 1}

Add the numbers

258 w^{4}

7 = 258 w^{4}

Swap the sides of the equation

258 w^{4} = 7

Divide both sides

\frac{258 w ^{4}}{258} = \frac{7}{258}

Divide the numbers

w^{4} = \frac{7}{258}

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

w = \pm 4 \frac{7}{258}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{258}

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

\frac{4 7}{4 258}

Multiply by the Conjugate

\frac{4 7 \times 4 25 8 ^{3}}{4 258 \times 4 25 8 ^{3}}

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

\frac{4 7 \times 25 8 ^{3}}{4 258 \times 4 25 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

4258 \times 4 25 8^{3}

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

4 258 \times 25 8^{3}

Calculate the product

4 25 8^{4}

Reduce the index of the radical and exponent with 4

258

\frac{4 7 \times 25 8 ^{3}}{258}

w = \pm \frac{4 7 \times 25 8 ^{3}}{258}

Separate the equation into 2 possible cases

w = \frac{4 7 \times 25 8 ^{3}}{258} w = - \frac{4 7 \times 25 8 ^{3}}{258}

Solution

w_{1} = - \frac{4 7 \times 25 8 ^{3}}{258}, w_{2} = \frac{4 7 \times 25 8 ^{3}}{258}

Alternative Form

w_{1} \approx - 0.405854, w_{2} \approx 0.405854

Show Solution