Solve (3^2*4)^3:(3*4^-2)^-1

$$( 3 ^ { 2 } \cdot 4 ) ^ { 3 } : ( 3 \cdot 4 ^ { - 2 } ) ^ { - 1 }$$

Evaluate

$$8748$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(9\times 4\right)^{3}}{\left(3\times 4^{-2}\right)^{-1}}$$

Multiply 9 and 4 to get 36.

$$\frac{36^{3}}{\left(3\times 4^{-2}\right)^{-1}}$$

Calculate 36 to the power of 3 and get 46656.

$$\frac{46656}{\left(3\times 4^{-2}\right)^{-1}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{46656}{\left(3\times \frac{1}{16}\right)^{-1}}$$

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\frac{46656}{\left(\frac{3}{16}\right)^{-1}}$$

Calculate \frac{3}{16} to the power of -1 and get \frac{16}{3}.

$$\frac{46656}{\frac{16}{3}}$$

Divide 46656 by \frac{16}{3} by multiplying 46656 by the reciprocal of \frac{16}{3}.

$$46656\times \frac{3}{16}$$

Multiply 46656 and \frac{3}{16} to get 8748.

$$8748$$

Factor

$$2^{2}\times 3^{7}$$