Given that 16𝑎 to the power of five 𝑏 squared plus 26𝑎 is equal to two 𝑎 multiplied by eight 𝑎 to the power of four 𝑏 squared plus 𝑘, what is the value of 𝑘?
In order to answer this question, we need to factorize the equation by taking out the highest common factor. In this case, the highest common factor is two 𝑎. This is because two is the highest common factor of 16 and 26. And 𝑎 is the only other term in both parts of the equation.
Dividing 16𝑎 to the power of five 𝑏 squared by two 𝑎 gives us eight 𝑎 to the power of four 𝑏 squared as 16 divided by two is equal to eight and 𝑎 to the power of five divided by 𝑎 is equal to 𝑎 to the power of four. This means that the first term inside our parentheses is eight 𝑎 to the power of four 𝑏 squared.
Dividing the second term 26𝑎 by two 𝑎 gives us an answer of 13 as 26 divided by two is 13 and 𝑎 divided by 𝑎 is one. 13 multiplied by one is equal to 13. This means that the second term inside the parentheses is 13 plus 13.
As 13 is in the same position as the 𝑘 in the question, we can say that 𝑘 is equal to 13. We can check this answer by multiplying our two 𝑎 outside the parentheses by the 13 inside the parentheses, which gives us 26𝑎, the term that we started with.