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}

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

Evaluate

$$\frac{53747712}{19}\approx 2828826.947368421$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate 4 to the power of 4 and get 256.

$$\frac{256\times 6^{11}}{6^{6}-4^{3}\times 6^{3}}$$

Calculate 6 to the power of 11 and get 362797056.

$$\frac{256\times 362797056}{6^{6}-4^{3}\times 6^{3}}$$

Multiply 256 and 362797056 to get 92876046336.

$$\frac{92876046336}{6^{6}-4^{3}\times 6^{3}}$$

Calculate 6 to the power of 6 and get 46656.

$$\frac{92876046336}{46656-4^{3}\times 6^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{92876046336}{46656-64\times 6^{3}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{92876046336}{46656-64\times 216}$$

Multiply 64 and 216 to get 13824.

$$\frac{92876046336}{46656-13824}$$

Subtract 13824 from 46656 to get 32832.

$$\frac{92876046336}{32832}$$

Reduce the fraction \frac{92876046336}{32832} to lowest terms by extracting and canceling out 1728.

$$\frac{53747712}{19}$$

Factor

$$\frac{2 ^ {13} \cdot 3 ^ {8}}{19} = 2828826\frac{18}{19} = 2828826.947368421$$