Solve sqrt{(-1/4)^2}*sqrt{(1/3)^2}=1/4*1/3

$$\sqrt { ( - \frac { 1 } { 4 } ) ^ { 2 } } \times \sqrt { ( \frac { 1 } { 3 } ) ^ { 2 } } = \frac { 1 } { 4 } \times \frac { 1 } { 3 }$$

Verify

Solution Steps

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{\frac{1}{16}}\sqrt{\left(\frac{1}{3}\right)^{2}}=\frac{1}{4}\times \frac{1}{3}$$

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{4}\sqrt{\left(\frac{1}{3}\right)^{2}}=\frac{1}{4}\times \frac{1}{3}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{4}\sqrt{\frac{1}{9}}=\frac{1}{4}\times \frac{1}{3}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{4}\times \frac{1}{3}=\frac{1}{4}\times \frac{1}{3}$$

Multiply \frac{1}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{4\times 3}=\frac{1}{4}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 3}.

$$\frac{1}{12}=\frac{1}{4}\times \frac{1}{3}$$

Multiply \frac{1}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{12}=\frac{1\times 1}{4\times 3}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 3}.

$$\frac{1}{12}=\frac{1}{12}$$

Compare \frac{1}{12} and \frac{1}{12}.

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