Solve 8^-10-5*05^10/2^-10-2^14leq0

$$\frac{ { 8 }^{ -10 } -5 \cdot 0 { 5 }^{ 10 } }{ { 2 }^{ -10 } - { 2 }^{ 14 } } \leq 0$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 10 to get 11.

$$\frac{8^{-10}-5^{11}\times 0}{2^{-10}-2^{14}}\leq 0$$

Calculate 8 to the power of -10 and get \frac{1}{1073741824}.

$$\frac{\frac{1}{1073741824}-5^{11}\times 0}{2^{-10}-2^{14}}\leq 0$$

Calculate 5 to the power of 11 and get 48828125.

$$\frac{\frac{1}{1073741824}-48828125\times 0}{2^{-10}-2^{14}}\leq 0$$

Multiply 48828125 and 0 to get 0.

$$\frac{\frac{1}{1073741824}-0}{2^{-10}-2^{14}}\leq 0$$

Subtract 0 from \frac{1}{1073741824} to get \frac{1}{1073741824}.

$$\frac{\frac{1}{1073741824}}{2^{-10}-2^{14}}\leq 0$$

Calculate 2 to the power of -10 and get \frac{1}{1024}.

$$\frac{\frac{1}{1073741824}}{\frac{1}{1024}-2^{14}}\leq 0$$

Calculate 2 to the power of 14 and get 16384.

$$\frac{\frac{1}{1073741824}}{\frac{1}{1024}-16384}\leq 0$$

Subtract 16384 from \frac{1}{1024} to get -\frac{16777215}{1024}.

$$\frac{\frac{1}{1073741824}}{-\frac{16777215}{1024}}\leq 0$$

Divide \frac{1}{1073741824} by -\frac{16777215}{1024} by multiplying \frac{1}{1073741824} by the reciprocal of -\frac{16777215}{1024}.

$$\frac{1}{1073741824}\left(-\frac{1024}{16777215}\right)\leq 0$$

Multiply \frac{1}{1073741824} and -\frac{1024}{16777215} to get -\frac{1}{17592184995840}.

$$-\frac{1}{17592184995840}\leq 0$$

Compare -\frac{1}{17592184995840} and 0.

$$\text{true}$$