Solve -18^{2}-36:[2^{8}:(-2^9)^7+(-9)^15:(-3*3^20)]

$$- 18 ^ { 2 } - 36 : [ 2 ^ { 8 } : ( - 2 ^ { 9 } ) ^ { 7 } + ( - 9 ) ^ { 15 } : ( - 3 \cdot 3 ^ { 20 } ) ]$$

Evaluate

$$-\frac{229767456035355444117180}{709154811724267782143}\approx -324.001828989$$

Solution Steps

Calculate 18 to the power of 2 and get 324.

$$-324-\frac{36}{\frac{2^{8}}{\left(-2^{9}\right)^{7}}+\frac{\left(-9\right)^{15}}{-3\times 3^{20}}}$$

Calculate 2 to the power of 8 and get 256.

$$-324-\frac{36}{\frac{256}{\left(-2^{9}\right)^{7}}+\frac{\left(-9\right)^{15}}{-3\times 3^{20}}}$$

Calculate 2 to the power of 9 and get 512.

$$-324-\frac{36}{\frac{256}{\left(-512\right)^{7}}+\frac{\left(-9\right)^{15}}{-3\times 3^{20}}}$$

Calculate -512 to the power of 7 and get -9223372036854775808.

$$-324-\frac{36}{\frac{256}{-9223372036854775808}+\frac{\left(-9\right)^{15}}{-3\times 3^{20}}}$$

Reduce the fraction \frac{256}{-9223372036854775808} to lowest terms by extracting and canceling out 256.

$$-324-\frac{36}{-\frac{1}{36028797018963968}+\frac{\left(-9\right)^{15}}{-3\times 3^{20}}}$$

Calculate -9 to the power of 15 and get -205891132094649.

$$-324-\frac{36}{-\frac{1}{36028797018963968}+\frac{-205891132094649}{-3\times 3^{20}}}$$

Calculate 3 to the power of 20 and get 3486784401.

$$-324-\frac{36}{-\frac{1}{36028797018963968}+\frac{-205891132094649}{-3\times 3486784401}}$$

Multiply -3 and 3486784401 to get -10460353203.

$$-324-\frac{36}{-\frac{1}{36028797018963968}+\frac{-205891132094649}{-10460353203}}$$

Divide -205891132094649 by -10460353203 to get 19683.

$$-324-\frac{36}{-\frac{1}{36028797018963968}+19683}$$

Add -\frac{1}{36028797018963968} and 19683 to get \frac{709154811724267782143}{36028797018963968}.

$$-324-\frac{36}{\frac{709154811724267782143}{36028797018963968}}$$

Divide 36 by \frac{709154811724267782143}{36028797018963968} by multiplying 36 by the reciprocal of \frac{709154811724267782143}{36028797018963968}.

$$-324-36\times \frac{36028797018963968}{709154811724267782143}$$

Multiply 36 and \frac{36028797018963968}{709154811724267782143} to get \frac{1297036692682702848}{709154811724267782143}.

$$-324-\frac{1297036692682702848}{709154811724267782143}$$

Subtract \frac{1297036692682702848}{709154811724267782143} from -324 to get -\frac{229767456035355444117180}{709154811724267782143}.

$$-\frac{229767456035355444117180}{709154811724267782143}$$

Factor

$$-\frac{229767456035355444117180}{709154811724267782143} = -324\frac{1.2970366926827028 \times 10^{18}}{7.091548117242678 \times 10^{20}} = -324.00182898948333$$