Solve 81/16=(2/3)^2|R

$$\frac { 81 } { 16 } = ( \frac { 2 } { 3 } ) ^ { 2 } | R$$

Solve for R

$$R = -\frac{729}{64} = -11\frac{25}{64} = -11.390625$$

$$R = \frac{729}{64} = 11\frac{25}{64} = 11.390625$$

Steps Using Definition of Absolute Value

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{81}{16}=\frac{4}{9}|R|$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{4}{9}|R|=\frac{81}{16}$$

Multiply both sides by \frac{9}{4}, the reciprocal of \frac{4}{9}.

$$|R|=\frac{81}{16}\times \frac{9}{4}$$

Multiply \frac{81}{16} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$|R|=\frac{81\times 9}{16\times 4}$$

Do the multiplications in the fraction \frac{81\times 9}{16\times 4}.

$$|R|=\frac{729}{64}$$

Use the definition of absolute value.

$$R=\frac{729}{64} R=-\frac{729}{64}$$