Solve a^2*b^2=(a*b)^4

Question

Solve the equation

Solve for a

Solve for b

a = 0 a = \frac{1}{∣ b ∣} a = - \frac{1}{∣ b ∣}

Evaluate

a^{2} b^{2} = (ab)^{4}

To raise a product to a power,raise each factor to that power

a^{2} b^{2} = a^{4} b^{4}

Rewrite the expression

b^{2} a^{2} = b^{4} a^{4}

Add or subtract both sides

b^{2} a^{2} - b^{4} a^{4} = 0

Factor the expression

b^{2} a^{2} (1 - b^{2} a^{2}) = 0

Divide both sides

a^{2} (1 - b^{2} a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 1 - b^{2} a^{2} = 0

The only way a power can be 0 is when the base equals 0

a = 0 1 - b^{2} a^{2} = 0

Solution

More Steps

Evaluate

1 - b^{2} a^{2} = 0

Move the constant to the right-hand side and change its sign

- b^{2} a^{2} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- b^{2} a^{2} = - 1

Divide both sides

\frac{- b ^{2} a ^{2}}{- b ^{2}} = \frac{- 1}{- b ^{2}}

Divide the numbers

a^{2} = \frac{- 1}{- b ^{2}}

Divide the numbers

a^{2} = \frac{1}{b ^{2}}

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

a = \pm \frac{1}{b ^{2}}

Simplify the expression

More Steps

Evaluate

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

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

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

Simplify the radical expression

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

Simplify the radical expression

\frac{1}{∣ b ∣}

a = \pm \frac{1}{∣ b ∣}

Separate the equation into 2 possible cases

a = \frac{1}{∣ b ∣} a = - \frac{1}{∣ b ∣}

a = 0 a = \frac{1}{∣ b ∣} a = - \frac{1}{∣ b ∣}

Show Solution