explain how 4^6 x 4^-9 simplified is 1/16

Answer 1

To simplify the expression 4^6 x 4^-9, we can combine the exponents by using the rule that states when multiplying numbers with the same base, you can add the exponents.

4^6 x 4^-9 = 4^(6-9) = 4^(-3)

Now, to simplify further, we can rewrite 4^-3 as 1/4^3, since a negative exponent indicates that the number is in the denominator of a fraction.

Therefore, 4^6 x 4^-9 = 1/(4^3) = 1/64

So, the simplified expression is 1/64 which is equivalent to 1/16.