Solve [5^1*3^3/3^2]^-3

$$[ \frac { 5 ^ { 1 } \cdot 3 ^ { 3 } } { 3 ^ { 2 } } ] ^ { - 3 }$$

Evaluate

$$\frac{1}{3375}\approx 0.000296296$$

Solution Steps

Cancel out 3^{2} in both numerator and denominator.

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

Expand \left(3\times 5^{1}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 1 and -3 to get -3.

$$3^{-3}\times 5^{-3}$$

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

$$\frac{1}{27}\times 5^{-3}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{1}{27}\times \frac{1}{125}$$

Multiply \frac{1}{27} and \frac{1}{125} to get \frac{1}{3375}.

$$\frac{1}{3375}$$

Factor

$$\frac{1}{3 ^ {3} \cdot 5 ^ {3}} = 0.0002962962962962963$$