Solve 4^2*5^-3*4^-3/4^5*{5^6}

$$\frac{ { 4 }^{ 2 } \times { 5 }^{ -3 } \times { 4 }^{ -3 } }{ { 4 }^{ 5 } \times { 5 }^{ 6 } }$$

Evaluate

$$\frac{1}{8000000000}=1.25 \cdot 10^{-10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{4^{-1}\times 5^{-3}}{4^{5}\times 5^{6}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{4^{6}\times 5^{9}}$$

Calculate 4 to the power of 6 and get 4096.

$$\frac{1}{4096\times 5^{9}}$$

Calculate 5 to the power of 9 and get 1953125.

$$\frac{1}{4096\times 1953125}$$

Multiply 4096 and 1953125 to get 8000000000.

$$\frac{1}{8000000000}$$

Factor

$$\frac{1}{2 ^ {12} \cdot 5 ^ {9}} = 1.25 \times 10^{-10}$$