Solve frac{3*2^{-2}-1}{2^-2+1}*(4^-2-3)+sqrt[20]{(-7)^20}-sqrt[13]{(-2)^13}

$$\frac { 3 \cdot 2 ^ { - 2 } - 1 } { 2 ^ { - 2 } + 1 } \cdot ( 4 ^ { - 2 } - 3 ) + \sqrt[ 20 ] { ( - 7 ) ^ { 20 } } - \sqrt[ 13 ] { ( - 2 ) ^ { 13 } }$$

Evaluate

$$\frac{767}{80}=9.5875$$

Solution Steps

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

$$\frac{3\times \frac{1}{4}-1}{2^{-2}+1}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\frac{3}{4}-1}{2^{-2}+1}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Subtract 1 from \frac{3}{4} to get -\frac{1}{4}.

$$\frac{-\frac{1}{4}}{2^{-2}+1}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

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

$$\frac{-\frac{1}{4}}{\frac{1}{4}+1}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$\frac{-\frac{1}{4}}{\frac{5}{4}}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Divide -\frac{1}{4} by \frac{5}{4} by multiplying -\frac{1}{4} by the reciprocal of \frac{5}{4}.

$$-\frac{1}{4}\times \frac{4}{5}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Multiply -\frac{1}{4} and \frac{4}{5} to get -\frac{1}{5}.

$$-\frac{1}{5}\left(4^{-2}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

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

$$-\frac{1}{5}\left(\frac{1}{16}-3\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Subtract 3 from \frac{1}{16} to get -\frac{47}{16}.

$$-\frac{1}{5}\left(-\frac{47}{16}\right)+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Multiply -\frac{1}{5} and -\frac{47}{16} to get \frac{47}{80}.

$$\frac{47}{80}+\sqrt[20]{\left(-7\right)^{20}}-\sqrt[13]{\left(-2\right)^{13}}$$

Calculate -7 to the power of 20 and get 79792266297612001.

$$\frac{47}{80}+\sqrt[20]{79792266297612001}-\sqrt[13]{\left(-2\right)^{13}}$$

Calculate \sqrt[20]{79792266297612001} and get 7.

$$\frac{47}{80}+7-\sqrt[13]{\left(-2\right)^{13}}$$

Add \frac{47}{80} and 7 to get \frac{607}{80}.

$$\frac{607}{80}-\sqrt[13]{\left(-2\right)^{13}}$$

Calculate -2 to the power of 13 and get -8192.

$$\frac{607}{80}-\sqrt[13]{-8192}$$

Calculate \sqrt[13]{-8192} and get -2.

$$\frac{607}{80}-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{607}{80}+2$$

Add \frac{607}{80} and 2 to get \frac{767}{80}.

$$\frac{767}{80}$$

Factor

$$\frac{13 \cdot 59}{2 ^ {4} \cdot 5} = 9\frac{47}{80} = 9.5875$$