Solve H=32^25^-8+64^-1/3

$$H = 32 ^ { 25 ^ { - 8 } } + 64 ^ { - 1 / 3 }$$

Solve for H

$$H=\sqrt[30517578125]{2}+\frac{1}{4}\approx 1.25$$

Steps for Solving Linear Equation

Calculate 25 to the power of -8 and get \frac{1}{152587890625}.

$$H=32^{\frac{1}{152587890625}}+64^{-\frac{1}{3}}$$

Calculate 64 to the power of -\frac{1}{3} and get \frac{1}{4}.

$$H=32^{\frac{1}{152587890625}}+\frac{1}{4}$$

Reorder the terms.

$$H=\sqrt[152587890625]{32}+\frac{1}{4}$$

Rewrite \sqrt[152587890625]{32} as \sqrt[152587890625]{2^{5}}. Convert from radical to exponential form and cancel out 5 in the exponent. Convert back to radical form.

$$\sqrt[152587890625]{32}=\sqrt[152587890625]{2^{5}}=2^{\frac{5}{152587890625}}=2^{\frac{1}{30517578125}}=\sqrt[30517578125]{2}$$

Insert the obtained value back in the expression.

$$H=\sqrt[30517578125]{2}+\frac{1}{4}$$

Assign H

$$H≔\sqrt[30517578125]{2}+\frac{1}{4}$$