Solve (4^8*4^2):(4^3*4):2^6

$$( 4 ^ { 8 } \times 4 ^ { 2 } ) : ( 4 ^ { 3 } \times 4 ) : 2 ^ { 6 }$$

Evaluate

$$64$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\frac{4^{10}}{4^{3}\times 4}}{2^{6}}$$

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

$$\frac{\frac{4^{10}}{4^{4}}}{2^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 10 to get 6.

$$\frac{4^{6}}{2^{6}}$$

Calculate 4 to the power of 6 and get 4096.

$$\frac{4096}{2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{4096}{64}$$

Divide 4096 by 64 to get 64.

$$64$$

Factor

$$2^{6}$$