Solve (3/2)^-2*(3/2)^3:(3/2)^4=

$$( \frac { 3 } { 2 } ) ^ { - 2 } \cdot ( \frac { 3 } { 2 } ) ^ { 3 } : ( \frac { 3 } { 2 } ) ^ { 4 } =$$

Evaluate

$$\frac{8}{27}\approx 0.296296296$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

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

Rewrite \left(\frac{3}{2}\right)^{4} as \left(\frac{3}{2}\right)^{1}\times \left(\frac{3}{2}\right)^{3}. Cancel out \left(\frac{3}{2}\right)^{1} in both numerator and denominator.

$$\frac{1}{\left(\frac{3}{2}\right)^{3}}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{1}{\frac{27}{8}}$$

Divide 1 by \frac{27}{8} by multiplying 1 by the reciprocal of \frac{27}{8}.

$$1\times \frac{8}{27}$$

Multiply 1 and \frac{8}{27} to get \frac{8}{27}.

$$\frac{8}{27}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {3}} = 0.2962962962962963$$