Solve y^-5-4^-2/4^-3+4^-4

$$\frac { y ^ { - 5 } - 4 ^ { - 2 } } { 4 ^ { - 3 } + 4 ^ { - 4 } }$$

Evaluate

$$-\frac{16}{5}+\frac{256}{5y^{5}}$$

Solution Steps

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

$$\frac{y^{-5}-\frac{1}{16}}{4^{-3}+4^{-4}}$$

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

$$\frac{y^{-5}-\frac{1}{16}}{\frac{1}{64}+4^{-4}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{y^{-5}-\frac{1}{16}}{\frac{1}{64}+\frac{1}{256}}$$

Add \frac{1}{64} and \frac{1}{256} to get \frac{5}{256}.

$$\frac{y^{-5}-\frac{1}{16}}{\frac{5}{256}}$$

Divide y^{-5}-\frac{1}{16} by \frac{5}{256} by multiplying y^{-5}-\frac{1}{16} by the reciprocal of \frac{5}{256}.

$$\frac{\left(y^{-5}-\frac{1}{16}\right)\times 256}{5}$$

Use the distributive property to multiply y^{-5}-\frac{1}{16} by 256.

$$\frac{256y^{-5}-16}{5}$$

Expand

$$-\frac{16}{5}+\frac{256}{5y^{5}}$$

Solution Steps

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

$$\frac{y^{-5}-\frac{1}{16}}{4^{-3}+4^{-4}}$$

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

$$\frac{y^{-5}-\frac{1}{16}}{\frac{1}{64}+4^{-4}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{y^{-5}-\frac{1}{16}}{\frac{1}{64}+\frac{1}{256}}$$

Add \frac{1}{64} and \frac{1}{256} to get \frac{5}{256}.

$$\frac{y^{-5}-\frac{1}{16}}{\frac{5}{256}}$$

Divide y^{-5}-\frac{1}{16} by \frac{5}{256} by multiplying y^{-5}-\frac{1}{16} by the reciprocal of \frac{5}{256}.

$$\frac{\left(y^{-5}-\frac{1}{16}\right)\times 256}{5}$$

Use the distributive property to multiply y^{-5}-\frac{1}{16} by 256.

$$\frac{256y^{-5}-16}{5}$$