Solve 1 / 2 7/9 = x^4 2/5x

Question

Solve the equation

x = \frac{5 7560}{6}

Alternative Form

x \approx 0.994382

Evaluate

\frac{1}{2} \times \frac{7}{9} = x^{4} \times \frac{2}{5} x

Multiply the numbers

More Steps

Evaluate

\frac{1}{2} \times \frac{7}{9}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7}{2 \times 9}

Multiply the numbers

\frac{7}{18}

\frac{7}{18} = x^{4} \times \frac{2}{5} x

Multiply

More Steps

Evaluate

x^{4} \times \frac{2}{5} x

Multiply the terms with the same base by adding their exponents

x^{4 + 1} \times \frac{2}{5}

Add the numbers

x^{5} \times \frac{2}{5}

Use the commutative property to reorder the terms

\frac{2}{5} x^{5}

\frac{7}{18} = \frac{2}{5} x^{5}

Swap the sides of the equation

\frac{2}{5} x^{5} = \frac{7}{18}

Multiply by the reciprocal

\frac{2}{5} x^{5} \times \frac{5}{2} = \frac{7}{18} \times \frac{5}{2}

Multiply

x^{5} = \frac{7}{18} \times \frac{5}{2}

Multiply

More Steps

Evaluate

\frac{7}{18} \times \frac{5}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7 \times 5}{18 \times 2}

Multiply the numbers

\frac{35}{18 \times 2}

Multiply the numbers

\frac{35}{36}

x^{5} = \frac{35}{36}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{35}{36}

Calculate

x = 5 \frac{35}{36}

Solution

More Steps

Evaluate

5 \frac{35}{36}

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

\frac{5 35}{5 36}

Multiply by the Conjugate

\frac{5 35 \times 5 3 6 ^{4}}{5 36 \times 5 3 6 ^{4}}

Simplify

\frac{5 35 \times 6 5 216}{5 36 \times 5 3 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

535 \times 65216

Multiply the terms

57560 \times 6

Use the commutative property to reorder the terms

657560

\frac{6 5 7560}{5 36 \times 5 3 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

536 \times 5 3 6^{4}

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

5 36 \times 3 6^{4}

Calculate the product

5 3 6^{5}

Transform the expression

5 6^{10}

Reduce the index of the radical and exponent with 5

6^{2}

\frac{6 5 7560}{6 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{6}{6 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{6 ^{2 - 1}}

Subtract the terms

\frac{1}{6 ^{1}}

Simplify

\frac{1}{6}

\frac{5 7560}{6}

x = \frac{5 7560}{6}

Alternative Form

x \approx 0.994382

Show Solution

Solve the equation

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