Solve [(-3/4)^{-2}]^2:[(-3/4)^2*(-3/4)^-3:(-3/4)^-2]

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

Evaluate

$$-\frac{1024}{243}\approx -4.21399177$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

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

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from -1 to get 1.

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

Rewrite \left(-\frac{3}{4}\right)^{1} as \left(-\frac{3}{4}\right)^{-4}\left(-\frac{3}{4}\right)^{5}. Cancel out \left(-\frac{3}{4}\right)^{-4} in both numerator and denominator.

$$\frac{1}{\left(-\frac{3}{4}\right)^{5}}$$

Calculate -\frac{3}{4} to the power of 5 and get -\frac{243}{1024}.

$$\frac{1}{-\frac{243}{1024}}$$

Divide 1 by -\frac{243}{1024} by multiplying 1 by the reciprocal of -\frac{243}{1024}.

$$1\left(-\frac{1024}{243}\right)$$

Multiply 1 and -\frac{1024}{243} to get -\frac{1024}{243}.

$$-\frac{1024}{243}$$

Factor

$$-\frac{1024}{243} = -4\frac{52}{243} = -4.2139917695473255$$