Question

Which expression is equivalent to 4^4 x 4^-9

Answer 1

The expression 4^4 x 4^-9 is equivalent to 1/1,024.

Step-by-step explanation:

To simplify the expression 4^4 x 4^-9, we need to apply the rule of exponents which states that when multiplying numbers with the same base, we add the exponents. First, simplify 4^4 as 4 x 4 x 4 x 4 = 256. Then, simplify 4^-9 as 1/4^9 = 1/262,144. Now we can multiply the two simplified expressions together:

256 x 1/262,144 = 1/1,024

Therefore, the expression 4^4 x 4^-9 is equivalent to 1/1,024.

Answer 2

`4^4*4^(-9)=4^(4+(-9))=4^(-5)=(1)/(4^5)=(1)/(1024)\\\\Used:\\\\a^n\cdot a^m=a^(n+m)\\\\a^(-n)=(1)/(a^n)`