Solve (2/3)^-2+(2/3)^-2:(2/3)^-6-(2/3)^0

$$( \frac { 2 } { 3 } ) ^ { - 2 } + ( \frac { 2 } { 3 } ) ^ { - 2 } : ( \frac { 2 } { 3 } ) ^ { - 6 } - ( \frac { 2 } { 3 } ) ^ { 0 }$$

Evaluate

$$\frac{469}{324}\approx 1.447530864$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -2 to get 4.

$$\left(\frac{2}{3}\right)^{-2}+\left(\frac{2}{3}\right)^{4}-\left(\frac{2}{3}\right)^{0}$$

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

$$\frac{9}{4}+\left(\frac{2}{3}\right)^{4}-\left(\frac{2}{3}\right)^{0}$$

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

$$\frac{9}{4}+\frac{16}{81}-\left(\frac{2}{3}\right)^{0}$$

Add \frac{9}{4} and \frac{16}{81} to get \frac{793}{324}.

$$\frac{793}{324}-\left(\frac{2}{3}\right)^{0}$$

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

$$\frac{793}{324}-1$$

Subtract 1 from \frac{793}{324} to get \frac{469}{324}.

$$\frac{469}{324}$$

Factor

$$\frac{7 \cdot 67}{2 ^ {2} \cdot 3 ^ {4}} = 1\frac{145}{324} = 1.4475308641975309$$