Simplify the Expression: a^y × a^x × 7^y × b^9 × a^6

Question

Solve the following problem:

ayax7yb9a6= a^ya^x7^yb^9a^6=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 When multiplying powers with equal bases
00:07 The power of the result equals the sum of the powers
00:12 We'll apply this formula to our exercise and then proceed to add together the powers
00:19 Let's calculate the power
00:24 This is the solution

Step-by-Step Solution

Begin by applying the distributive property of multiplication and proceed to arrange the algebraic expression according to like bases:

ayaxa6 b97y a^ya^xa^{6\text{ }}b^97^y

Next, we'll use the power rule to multiply terms with the same base:

aman=am+n a^m\cdot a^n=a^{m+n}

Note that this rule applies to any number of terms in multiplication, not just two. For example, when multiplying three terms with the same base, we obtain the following:

amanak=am+nak=am+n+k a^m\cdot a^n\cdot a^k=a^{m+n}\cdot a^k=a^{m+n+k}

Therefore, we can combine all terms with the same base under one base:

ay+x+6b97y a^{y+x+6}b^97^y

Note that we could only combine terms with identical bases using this rule,

From here we can see that the expression cannot be simplified further, and therefore this is the correct answer, which is answer C (since the distributive property of multiplication holds).

Answer

ay+x+67yb9 a^{y+x+6}7^yb^9