Solve (4^2)(4^2)/(4^3)^2*4=

$$\frac { ( 4 ^ { 2 } ) ( 4 ^ { 2 } ) } { ( 4 ^ { 3 } ) ^ { 2 } \cdot 4 } =$$

Evaluate

$$\frac{1}{64}=0.015625$$

Solution Steps

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

$$\frac{4^{4}}{\left(4^{3}\right)^{2}\times 4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{4^{4}}{4^{6}\times 4}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{4^{4}}{4^{7}}$$

Rewrite 4^{7} as 4^{4}\times 4^{3}. Cancel out 4^{4} in both numerator and denominator.

$$\frac{1}{4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{1}{64}$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$