Solve frac{(4^{2})^{3}*6^{3}*6^{2}*(6^{2})^{3}*4^{0}*4^{-2}}{(6^{3})^2*4^-2*4^5*6^3}

$$\frac { ( 4 ^ { 2 } ) ^ { 3 } \times 6 ^ { 3 } \times 6 ^ { 2 } \times ( 6 ^ { 2 } ) ^ { 3 } \times 4 ^ { 0 } \times 4 ^ { - 2 } } { ( 6 ^ { 3 } ) ^ { 2 } \times 4 ^ { - 2 } \times 4 ^ { 5 } \times 6 ^ { 3 } }$$

Evaluate

$$144$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times \left(6^{2}\right)^{3}\times 4^{0}\times 4^{-2}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times 6^{6}\times 4^{0}\times 4^{-2}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 0 to get 6.

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times 6^{6}\times 4^{-2}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and -2 to get 4.

$$\frac{4^{4}\times 6^{3}\times 6^{2}\times 6^{6}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{4^{4}\times 6^{5}\times 6^{6}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{4^{4}\times 6^{11}}{\left(6^{3}\right)^{2}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{4^{4}\times 6^{11}}{6^{6}\times 4^{-2}\times 4^{5}\times 6^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{4^{4}\times 6^{11}}{6^{9}\times 4^{-2}\times 4^{5}}$$

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{4^{4}\times 6^{11}}{6^{9}\times 4^{3}}$$

Cancel out 4^{3}\times 6^{9} in both numerator and denominator.

$$4\times 6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$4\times 36$$

Multiply 4 and 36 to get 144.

$$144$$

Factor

$$2^{4}\times 3^{2}$$