Question

Ellie wants to rewrite the expression (a2)2 ∙ (a3)2 as a single exponent of the form an. She claims that n = 36 because 22 · 32 = 4 · 9 = 36. Decide if Ellie is correct. If she is correct, enter 36 below. If she is not correct, enter the correct value of n.

Answer 1

Answer: Hello!

you writted the equation (a2)2 ∙ (a3)2, wich i tink means:

((a^2)^2)*((a^3)^2)

First let's write some relations:

`(x^(a) )^(b)  = x^(a*b)`

`x^(a)*x^(b)  = x^(a+b)`

Now we have the equation

`(a^(2) )^(2) *(a^(3) )^(2) = a^(2*2) *a^(3*2) = a^(4) * a^(6) = a^(6 + 4) = a^(10)`

Then Ellie is incorrect, the correct exponent of the simplification is n = 10.

Answer 2

No, Ellie is not correct.
Please assume that I am writing in terms of exponents:
The expression (a2)2. (a3)2 = (a)4.(a)6 [since 2. 2 = 4 and 3. 2 = 6]
= (a)(4+6) [since product of a term with different
exponents is equal to the term raised to the
power of the sum of the exponents]
=(a)10
Therefore the answer is n=10