Solve 4^2 6^2=(r^3)^2

Question

Solve the equation

r_{1} = - 233, r_{2} = 233

Alternative Form

r_{1} \approx - 2.884499, r_{2} \approx 2.884499

Evaluate

4^{2} \times 6^{2} = (r^{3})^{2}

Multiply the numbers

More Steps

Evaluate

4^{2} \times 6^{2}

Multiply the terms with equal exponents by multiplying their bases

(4 \times 6)^{2}

Multiply the numbers

2 4^{2}

2 4^{2} = (r^{3})^{2}

Simplify

More Steps

Evaluate

(r^{3})^{2}

Multiply the exponents

r^{3 \times 2}

Multiply the numbers

r^{6}

2 4^{2} = r^{6}

Swap the sides of the equation

r^{6} = 2 4^{2}

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

r = \pm 6 2 4^{2}

Simplify the expression

r = \pm 324

Separate the equation into 2 possible cases

r = 324 r = - 324

Calculate

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

r = 233 r = - 324

Calculate

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

r = 233 r = - 233

Solution

r_{1} = - 233, r_{2} = 233

Alternative Form

r_{1} \approx - 2.884499, r_{2} \approx 2.884499

Show Solution

Rewrite the equation

x^{6} + 3 x^{4} y^{2} + 3 x^{2} y^{4} + y^{6} = 576

Evaluate

4^{2} \times 6^{2} = (r^{3})^{2}

Evaluate

More Steps

Evaluate

4^{2} \times 6^{2}

Multiply the terms with equal exponents by multiplying their bases

(4 \times 6)^{2}

Multiply the numbers

2 4^{2}

Evaluate the power

576

576 = (r^{3})^{2}

Evaluate

More Steps

Evaluate

(r^{3})^{2}

Multiply the exponents

r^{3 \times 2}

Multiply the numbers

r^{6}

576 = r^{6}

Rewrite the expression

- r^{6} = - 576

Divide both sides of the equation by - 1

r^{6} = 576

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

(x^{2} + y^{2})^{3} = 576

Solution

x^{6} + 3 x^{4} y^{2} + 3 x^{2} y^{4} + y^{6} = 576

Show Solution

Solve the equation

Rewrite the equation

Graph