Solve (1/3)^{3}*(-1/3)^{5}*(-1/3)^{2}]^{3}:[-(-1/3)^{7}]^4-(-frac{1}{3})^2-(-frac{3}{13})^4*(frac{13}{9})^4

$$( \frac { 1 } { 3 } ) ^ { 3 } \cdot ( - \frac { 1 } { 3 } ) ^ { 5 } \cdot ( - \frac { 1 } { 3 } ) ^ { 2 } ] ^ { 3 } : [ - ( - \frac { 1 } { 3 } ) ^ { 7 } ] ^ { 4 } - ( - \frac { 1 } { 3 } ) ^ { 2 } - ( - \frac { 3 } { 13 } ) ^ { 4 } \cdot ( \frac { 13 } { 9 } ) ^ { 4 }$$

Evaluate

$$-\frac{1}{59049}\approx -0.000016935$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\left(\frac{1}{3}\right)^{3}\left(-\frac{1}{3}\right)^{7}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{1}{27}\left(-\frac{1}{3}\right)^{7}$$

Calculate -\frac{1}{3} to the power of 7 and get -\frac{1}{2187}.

$$\frac{1}{27}\left(-\frac{1}{2187}\right)$$

Multiply \frac{1}{27} times -\frac{1}{2187} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-1\right)}{27\times 2187}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{27\times 2187}.

$$\frac{-1}{59049}$$

Fraction \frac{-1}{59049} can be rewritten as -\frac{1}{59049} by extracting the negative sign.

$$-\frac{1}{59049}$$

Factor

$$-\frac{1}{59049} = -1.6935087808430285 \times 10^{-5}$$