Solve (frac{4^{3}*4^2}{4^4})^2=4^2

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

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\left(4^{1}\right)^{2}=4^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 2 to get 2.

$$4^{2}=4^{2}$$

As 4^{2} and 4^{2} have the same base, compare them by comparing their exponents.

$$\text{true}$$