Solve x^2 y^2 8xy=90 a

Question

Solve the equation

Solve for x

Solve for a

Solve for y

x = \frac{3 90 a}{2 y}

Evaluate

x^{2} y^{2} \times 8 x y = 90 a

Multiply

More Steps

Evaluate

x^{2} y^{2} \times 8 x y

Multiply the terms with the same base by adding their exponents

x^{2 + 1} y^{2} \times 8 y

Add the numbers

x^{3} y^{2} \times 8 y

Multiply the terms with the same base by adding their exponents

x^{3} y^{2 + 1} \times 8

Add the numbers

x^{3} y^{3} \times 8

Use the commutative property to reorder the terms

8 x^{3} y^{3}

8 x^{3} y^{3} = 90 a

Rewrite the expression

8 y^{3} x^{3} = 90 a

Divide both sides

\frac{8 y ^{3} x ^{3}}{8 y ^{3}} = \frac{90 a}{8 y ^{3}}

Divide the numbers

x^{3} = \frac{90 a}{8 y ^{3}}

Cancel out the common factor 2

x^{3} = \frac{45 a}{4 y ^{3}}

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

3 x^{3} = 3 \frac{45 a}{4 y ^{3}}

Calculate

x = 3 \frac{45 a}{4 y ^{3}}

Solution

More Steps

Evaluate

3 \frac{45 a}{4 y ^{3}}

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

\frac{3 45 a}{3 4 y ^{3}}

Simplify the radical expression

More Steps

Evaluate

3 4 y^{3}

Rewrite the expression

34 \times 3 y^{3}

Simplify the root

34 \times y

\frac{3 45 a}{3 4 \times y}

Multiply by the Conjugate

\frac{3 45 a \times 3 4 ^{2}}{3 4 \times y 3 4 ^{2}}

Calculate

\frac{3 45 a \times 3 4 ^{2}}{2 ^{2} y}

Calculate

More Steps

Evaluate

3 45 a \times 3 4^{2}

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

3 45 a \times 4^{2}

Calculate the product

3 720 a

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

3 8 \times 90 a

Write the number in exponential form with the base of 2

3 2^{3} \times 90 a

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

3 2^{3} \times 3 90 a

Reduce the index of the radical and exponent with 3

2 3 90 a

\frac{2 3 90 a}{2 ^{2} y}

Reduce the fraction

More Steps

Calculate

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

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

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

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 90 a}{2 y}

x = \frac{3 90 a}{2 y}

Show Solution