Solve 4^{2}*4^{2}:4^2*(2^2)^2=4^2

$$4 ^ { 2 } \cdot 4 ^ { 2 } : 4 ^ { 2 } \cdot ( 2 ^ { 2 } ) ^ { 2 } = 4 ^ { 2 }$$

Verify

Solution Steps

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4^{2}\times 2^{4}=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\times 2^{4}=4^{2}$$

Calculate 2 to the power of 4 and get 16.

$$16\times 16=4^{2}$$

Multiply 16 and 16 to get 256.

$$256=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$256=16$$

Compare 256 and 16.

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