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EXPLANATION of SELECT DIFFICULT HW QUESTIONS Algebra Homework from Thursday Sept 10 ,2015 Pgs 431 and 436 Pg 431 question 48 2n × 2n+2 × 2 = 2n × 2n+2 × 21 = Rule: When multiplying expressions with the same bases, just add the exponents. The exponents are: n + n + 2 +1 = 2n + 3 so the answer becomes: 22n+3 Let's check this using a small #. Let n = 3. 23 × 23+2 × 2 = 8 × 25 × 2 = Now what about 22n+3 = 2 2(3)+3 = 2 6+3 = 29 = 512 Pg 431 question 52 5 x+1 x 5 1-x Just add up the exponents so x+ 1 + 1 – x = 2 So the answer is 52 or 25. 8 x 32 x 2 = 512 Pg 436 question 22 (3n-6)-4 So there were 2 things in question here. 1st, since we are raising a power to another power, we need to multiply the exponents. If there are negative exponents, simplify or combine the exponents before you create fractions. Also, since there is a coefficient inside the parenthesis, this too needs to be raised to the exponent outside the parenthesis. So now we have 3-4n-6(-4) = ( 1 81 ) n24 = n24 / 81 Pg 436 question 24 (5y 1/2)4 Here too, we have a coefficient inside the parenthesis that needs to be raised to the 4th power. 54y2 = 625y2 Pg 436 question 28 (r 2/5 s)5 So here, we just have to make sure we multiply the 2/5 exponent by 5. = r(2/5)5 s5 = r2s5