How does 2^(2x+1I

Question

transform into 2(2^x)^2? 

 

 

Answer 1

The expression is 2(2^x)² .

To transform2(2^x)² into 2^{2x + 1}.

Recall the formula : (a^m)ⁿ = a^mn.

2(2^x)² = 2 * (2^2x).

Recall the formula : a^m * aⁿ = a^{m + n}.

2(2^x)² = 2^{2x + 1}.

Answer 2

The expression is 2^{(2x + 1)}.

Apply Product of Powers : a^m · aⁿ = a^{m + n}.

2^{(2x + 1)} = 2^(2x) · 2¹.

Apply Power of a Power: : (a^m)ⁿ = a^{m · n}.

2^{(2x + 1)} = (2^x)² · 2¹.

2^{(2x + 1)} = 2(2^x)².