Solve frac{3^{4}*4^{-1}*3^-2*4^5}{3^-1*4^4}

$$\frac { 3 ^ { 4 } \cdot 4 ^ { - 1 } \cdot 3 ^ { - 2 } \cdot 4 ^ { 5 } } { 3 ^ { - 1 } \cdot 4 ^ { 4 } }$$

Evaluate

$$27$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

$$\frac{3^{2}\times 4^{-1}\times 4^{5}}{3^{-1}\times 4^{4}}$$

To multiply powers of the same base, add their exponents. Add -1 and 5 to get 4.

$$\frac{3^{2}\times 4^{4}}{3^{-1}\times 4^{4}}$$

Cancel out 4^{4} in both numerator and denominator.

$$\frac{3^{2}}{\frac{1}{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$3^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27$$

Factor

$$3^{3}$$