What is 2^{2x-3}+2^{2x+5} ?

The solution to 2^{2x-3}+2^{2x+5} is 257*2^{2x-3}

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simplify 2^{2x-3}+2^{2x+5}

simplify

2^{2 x - 3} + 2^{2 x + 5}

257 \cdot 2^{2 x - 3}

Solution steps

2^{2 x - 3} + 2^{2 x + 5}

2^{2 x + 5} = 2^{2 x - 3 + 8}

= 2^{2 x - 3} + 2^{2 x - 3 + 8}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

2^{2 x - 3 + 8} = 2^{8} \cdot 2^{2 x - 3}

= 2^{2 x - 3} + 2^{8} \cdot 2^{2 x - 3}

Factor out common term

2^{2 x - 3}

= 2^{2 x - 3} (1 + 2^{8})

Refine

= 257 \cdot 2^{2 x - 3}

(sin^{3} (x))^{2}

- 4 x^{2} + 25 y^{2}

3062 x^{9} + 30 y^{3} + 8

(- d)^{- 4}

4 x^{2} - b^{2}