Solve (2/3)^{2}*(-2/3)^{3}*(-2/3)^{4}]^{2}:[-(-2/3)^5]^3+(-frac{2}{3})^3-(frac{2}{7})^4

$$( \frac { 2 } { 3 } ) ^ { 2 } \cdot ( - \frac { 2 } { 3 } ) ^ { 3 } \cdot ( - \frac { 2 } { 3 } ) ^ { 4 } ] ^ { 2 } : [ - ( - \frac { 2 } { 3 } ) ^ { 5 } ] ^ { 3 } + ( - \frac { 2 } { 3 } ) ^ { 3 } - ( \frac { 2 } { 7 } ) ^ { 4 }$$

Evaluate

$$-\frac{512}{19683}\approx -0.026012295$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(\frac{2}{3}\right)^{2}\left(-\frac{2}{3}\right)^{7}$$

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

$$\frac{4}{9}\left(-\frac{2}{3}\right)^{7}$$

Calculate -\frac{2}{3} to the power of 7 and get -\frac{128}{2187}.

$$\frac{4}{9}\left(-\frac{128}{2187}\right)$$

Multiply \frac{4}{9} times -\frac{128}{2187} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-128\right)}{9\times 2187}$$

Do the multiplications in the fraction \frac{4\left(-128\right)}{9\times 2187}.

$$\frac{-512}{19683}$$

Fraction \frac{-512}{19683} can be rewritten as -\frac{512}{19683} by extracting the negative sign.

$$-\frac{512}{19683}$$

Factor

$$-\frac{512}{19683} = -0.02601229487374892$$