Rewrite the numerator using the exponent rule a^m+n = a^m * a^n.

You're on a roll — Question 1.1.1 Step 1: Rewrite the numerator using the exponent rule a^m+n = a^m · a^n. 2^x+5 + 2^x2^x = (2^x · 2^5 + 2^x)/(2^x) Step 2: Factor out the common term 2^x from the numerator. (2^x(2^5 + 1))/(2^x) Step 3: Cancel out the common term 2^x from the numerator and denominator. 2^5 + 1 Step 4: Calculate the value. 32 + 1 = 33 Question 1.1.2 Step 1: Rewrite the terms in the numerator to have a common factor. 2(2^2x) - 7 · 2^2x-12^2x-3 = 2^2x+1 - 7 · 2^2x-12^2x-3 Step 2: Express 2^2x+1 as 2^2x-1 · 2^2. 2^2x-1 · 2^2 - 7 · 2^2x-12^2x-3 Step 3: Factor out 2^2x-1 from the numerator. 2^2x-1(2^2 - 7)2^2x-3 = 2^2x-1(4 - 7)2^2x-3 Step 4: Simplify the expression in the parenthesis. 2^2x-1(-3)2^2x-3 Step 5: Use the exponent rule (a^m)/(a^n) = a^m-n. -3 · 2^(2x-1) - (2x-3) Step 6: Simplify the exponent. -3 · 2^2x-1-2x+3 = -3 · 2^2 Step 7: Calculate the final value. -3 · 4 = -12 Question 1.2.1 Step 1: Rearrange the equation into standard quadratic form ax^2 + bx + c = 0. x^2 - 24 = 5x x^2 - 5x - 24 = 0 Step 2: Factor the quadratic expression. Find two numbers that multiply to -24 and add to -5 (these are -8 and 3). (x-8)(x+3) = 0 Step 3: Set each factor equal to zero and solve for x. x-8 = 0 x = 8 x+3 = 0 x = -3 The solutions are x=8 or x=-3. Question 1.2.2 Step 1: Square both sides of the equation to eliminate the square root. sqrt(2x-1) = 3 (sqrt(2x-1))^2 = 3^2 2x-1 = 9 Step 2: Add 1 to both sides of the equation. 2x = 9 + 1 2x = 10 Step 3: Divide by 2 to solve for x. x = (10)/(2) x = 5 What's next?