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