Solve (2/3)^11*(-3/2)^12

$$( \frac { 2 } { 3 } ) ^ { 11 } \times ( - \frac { 3 } { 2 } ) ^ { 12 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Calculate \frac{2}{3} to the power of 11 and get \frac{2048}{177147}.

$$\frac{2048}{177147}\left(-\frac{3}{2}\right)^{12}$$

Calculate -\frac{3}{2} to the power of 12 and get \frac{531441}{4096}.

$$\frac{2048}{177147}\times \frac{531441}{4096}$$

Multiply \frac{2048}{177147} times \frac{531441}{4096} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2048\times 531441}{177147\times 4096}$$

Do the multiplications in the fraction \frac{2048\times 531441}{177147\times 4096}.

$$\frac{1088391168}{725594112}$$

Reduce the fraction \frac{1088391168}{725594112} to lowest terms by extracting and canceling out 362797056.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$