Solve frac{2^{3}*5^-15*2^7}{2^5*(2*5)^5}=

$$\frac { 2 ^ { 3 } \times 5 ^ { - 15 } \times 2 ^ { 7 } } { 2 ^ { 5 } \times ( 2 \times 5 ) ^ { 5 } } =$$

Evaluate

$$\frac{1}{95367431640625}=1.048576 \cdot 10^{-14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{2^{10}\times 5^{-15}}{2^{5}\times \left(2\times 5\right)^{5}}$$

Cancel out 2^{5} in both numerator and denominator.

$$\frac{2^{5}\times 5^{-15}}{\left(2\times 5\right)^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32\times 5^{-15}}{\left(2\times 5\right)^{5}}$$

Calculate 5 to the power of -15 and get \frac{1}{30517578125}.

$$\frac{32\times \frac{1}{30517578125}}{\left(2\times 5\right)^{5}}$$

Multiply 32 and \frac{1}{30517578125} to get \frac{32}{30517578125}.

$$\frac{\frac{32}{30517578125}}{\left(2\times 5\right)^{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{32}{30517578125}}{10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\frac{32}{30517578125}}{100000}$$

Express \frac{\frac{32}{30517578125}}{100000} as a single fraction.

$$\frac{32}{30517578125\times 100000}$$

Multiply 30517578125 and 100000 to get 3051757812500000.

$$\frac{32}{3051757812500000}$$

Reduce the fraction \frac{32}{3051757812500000} to lowest terms by extracting and canceling out 32.

$$\frac{1}{95367431640625}$$

Factor

$$\frac{1}{5 ^ {20}} = 1.048576 \times 10^{-14}$$