Solve 8^3*8^-4/8^-2*8^6

$$\frac { 8 ^ { 3 } \cdot 8 ^ { - 4 } } { 8 ^ { - 2 } \cdot 8 ^ { 6 } }$$

Evaluate

$$\frac{1}{32768}\approx 0.000030518$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{8^{-1}}{8^{-2}\times 8^{6}}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$\frac{8^{-1}}{8^{4}}$$

Rewrite 8^{4} as 8^{-1}\times 8^{5}. Cancel out 8^{-1} in both numerator and denominator.

$$\frac{1}{8^{5}}$$

Calculate 8 to the power of 5 and get 32768.

$$\frac{1}{32768}$$

Factor

$$\frac{1}{2 ^ {15}} = 3.0517578124999996 \times 10^{-5}$$