Solve {100}^{32^-25^-8^-3^-1}+{8}^{{9}^{-{2}^{-1}}}+{16}^{16^-{4^-{4^-0}}}

$${ 100 }^{ { 32 }^{ - { 25 }^{ - { 8 }^{ - { 3 }^{ -1 } } } } } + { 8 }^{ { 9 }^{ - { 2 }^{ -1 } } } + { 16 }^{ { 16 }^{ - { 4 }^{ - { 4 }^{ -0 } } } }$$

Evaluate

$$16$$

Solution Steps

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

$$100^{32^{-25^{-8^{-\frac{1}{3}}}}}+8^{9^{-2^{-1}}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 8 to the power of -\frac{1}{3} and get \frac{1}{2}.

$$100^{32^{-25^{-\frac{1}{2}}}}+8^{9^{-2^{-1}}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 25 to the power of -\frac{1}{2} and get \frac{1}{5}.

$$100^{32^{-\frac{1}{5}}}+8^{9^{-2^{-1}}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 32 to the power of -\frac{1}{5} and get \frac{1}{2}.

$$100^{\frac{1}{2}}+8^{9^{-2^{-1}}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 100 to the power of \frac{1}{2} and get 10.

$$10+8^{9^{-2^{-1}}}+16^{16^{-4^{-4^{0}}}}$$

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

$$10+8^{9^{-\frac{1}{2}}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.

$$10+8^{\frac{1}{3}}+16^{16^{-4^{-4^{0}}}}$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$10+2+16^{16^{-4^{-4^{0}}}}$$

Add 10 and 2 to get 12.

$$12+16^{16^{-4^{-4^{0}}}}$$

Calculate 4 to the power of 0 and get 1.

$$12+16^{16^{-4^{-1}}}$$

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

$$12+16^{16^{-\frac{1}{4}}}$$

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

$$12+16^{\frac{1}{2}}$$

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

$$12+4$$

Add 12 and 4 to get 16.

$$16$$

Factor

$$2^{4}$$