Solve [4^{7}*4^10*4]^2/(4^5)^7

$$[ 4 ^ { 7 } \cdot 4 ^ { 10 } \cdot 4 ] ^ { 2 } / ( 4 ^ { 5 } ) ^ { 7 }$$

Evaluate

$$4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 10 to get 17.

$$\frac{\left(4^{17}\times 4\right)^{2}}{\left(4^{5}\right)^{7}}$$

To multiply powers of the same base, add their exponents. Add 17 and 1 to get 18.

$$\frac{\left(4^{18}\right)^{2}}{\left(4^{5}\right)^{7}}$$

To raise a power to another power, multiply the exponents. Multiply 18 and 2 to get 36.

$$\frac{4^{36}}{\left(4^{5}\right)^{7}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 7 to get 35.

$$\frac{4^{36}}{4^{35}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 35 from 36 to get 1.

$$4^{1}$$

Calculate 4 to the power of 1 and get 4.

$$4$$

Factor

$$2^{2}$$