Solve |x^3| |x^4|=7

Evaluate

x^{3} x^{4} = 7

Simplify

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x^{4} x^{3} = 7

Separate the equation into 2 possible cases

x^{4} \times x^{3} = 7, x^{3} \geq 0 x^{4} (- x^{3}) = 7, x^{3} < 0

Evaluate

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x = 77, x^{3} \geq 0 x^{4} (- x^{3}) = 7, x^{3} < 0

The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0

x = 77, x \geq 0 x^{4} (- x^{3}) = 7, x^{3} < 0

Evaluate

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x = 77, x \geq 0 x = - 77, x^{3} < 0

The only way a base raised to an odd power can be less than 0 is if the base is less than 0

x = 77, x \geq 0 x = - 77, x < 0

Find the intersection

x = 77 x = - 77, x < 0

Find the intersection

x = 77 x = - 77

Solution

x_{1} = - 77, x_{2} = 77

Alternative Form

x_{1} \approx - 1.320469, x_{2} \approx 1.320469

Solve the equation