Solve (2/3)^4*(3/2)^7:(3/2)^3=(2/3)^0

$$( \frac { 2 } { 3 } ) ^ { 4 } \cdot ( \frac { 3 } { 2 } ) ^ { 7 } : ( \frac { 3 } { 2 } ) ^ { 3 } = ( \frac { 2 } { 3 } ) ^ { 0 }$$

Verify

Solution Steps

Cancel out \left(\frac{3}{2}\right)^{3} in both numerator and denominator.

$$\left(\frac{2}{3}\right)^{4}\times \left(\frac{3}{2}\right)^{4}=\left(\frac{2}{3}\right)^{0}$$

Calculate \frac{2}{3} to the power of 0 and get 1.

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

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}\times \left(\frac{3}{2}\right)^{4}=1$$

Calculate \frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{16}{81}\times \frac{81}{16}=1$$

Multiply \frac{16}{81} and \frac{81}{16} to get 1.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$