If Mr. K is 3 times older than Mr. M, the expression we use to solve an equation would be "K is 3x Mr. M" which translates to this mathematical expression: K=3M. Their ages added together is 88. So K + M = 88. But we already know that K = 3M, so we will sub it into the second equation to get 3M + M = 88 and 4M=88. M = 22. So if M = 22, then K = 3(22) which is 66. Therefore, Mr. K is 66 and Mr. M is 22. In number 11a, you have to follow the power rule for exponents which says that if we raise a power to a power, we multiply the powers together to get the new power. 5msquared all squared is 5m^4. n to the fifth all squared is n^(5*2) which is 10. So our new expression is
. In 11b, the rule is that when we multiply like bases (here our bases are a and b), we add the exponents. Since that whole thing in 11b represents everything being multiplied together, we will add the exponents on all the a's and put them with a single a, and then we will add the exponents on all the b's and put them with a single b. The exponents on all the a's add up to 8 (don't forget that an a without an exponent indicates a "1", NOT a 0!), and all the exponents on the b's add up to 11. So our simplified expression is
. In 11c, we have a quotient, and the rule for that is we will subtract the exponents on like bases, denominator from numerator. First of all, 35/7 = 5. That was the easy part. The exponent on the top x is 3 and the bottom x is 8, so we have the exponent as 3-8 which is -5. The exponent on the top y is 7 and the bottom y is 4 so our exponent is 7-4=3. Rewriting that as a single expression (I'm going to keep the negative exponent in it since it doesn't say to express all the exponents as positive) is
. In the last one we deal with negative exponents. In order to make a negative exponent positive, we put the base it's on under a 1 (keep in mind that bases can be variable OR numbers). In general,
. Our base is a 4, so we can rewrite it as
