Solve 7/6=8/w^3 - ScanMath

Question

Solve the equation

w = \frac{2 3 294}{7}

Alternative Form

w \approx 1.899829

Evaluate

\frac{7}{6} = \frac{8}{w ^{3}}

Find the domain

More Steps

Evaluate

w^{3} \neq = 0

The only way a power can not be 0 is when the base not equals 0

w \neq = 0

\frac{7}{6} = \frac{8}{w ^{3}}, w \neq = 0

Swap the sides of the equation

\frac{8}{w ^{3}} = \frac{7}{6}

Rewrite the expression

w^{3} = \frac{8 \times 6}{7}

Divide the terms

w^{3} = \frac{48}{7}

Take the 3 -th root on both sides of the equation

3 w^{3} = 3 \frac{48}{7}

Calculate

w = 3 \frac{48}{7}

Simplify the root

More Steps

Evaluate

3 \frac{48}{7}

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

\frac{3 48}{3 7}

Simplify the radical expression

More Steps

Evaluate

348

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{2 3 6}{3 7}

Multiply by the Conjugate

\frac{2 3 6 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{2 3 6 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 349

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

3 6 \times 49

Calculate the product

3294

\frac{2 3 294}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{2 3 294}{7}

w = \frac{2 3 294}{7}

Check if the solution is in the defined range

w = \frac{2 3 294}{7}, w \neq = 0

Solution

w = \frac{2 3 294}{7}

Alternative Form

w \approx 1.899829

Show Solution