Solve (4^{5}*4*4^3)^6:(4^4*4)^10=

$$( 4 ^ { 5 } \cdot 4 \cdot 4 ^ { 3 } ) ^ { 6 } : ( 4 ^ { 4 } \cdot 4 ) ^ { 10 } =$$

Evaluate

$$256$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\left(4^{6}\times 4^{3}\right)^{6}}{\left(4^{4}\times 4\right)^{10}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\left(4^{9}\right)^{6}}{\left(4^{4}\times 4\right)^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 6 to get 54.

$$\frac{4^{54}}{\left(4^{4}\times 4\right)^{10}}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{4^{54}}{\left(4^{5}\right)^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 10 to get 50.

$$\frac{4^{54}}{4^{50}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 50 from 54 to get 4.

$$4^{4}$$

Calculate 4 to the power of 4 and get 256.

$$256$$

Factor

$$2^{8}$$