The product of 3^4*3^-2 is
so I multiplied the exponents and got
4*-2
=-8
so my answer is 3^-8
Is this correct?
Thanks for checking my work
a ^ m * a ^ n = a ^ ( m + n )
3 ^ 4 * 3 ^ ( - 2 ) = 3 ^ [ 4 + ( - 2 ) ] = 3 ^ ( 4 - 2 ) = 3 ^ 2 = 9
OR
3 ^ 4 = 81
3 ^ ( - 2 ) = 1 / 3 ^ 2 = 1 / 9
3 ^ 4 * 3 ^ ( - 2 ) = 81 * 1 / 9 = 81 / 9 = 9
thank you I see my mistake.
I multiplied the exponents instead of adding them.
Thanks for correcting it for me.
To determine whether your answer is correct, let's simplify the expression step by step.
We start with the expression 3^4 * 3^(-2).
When multiplying two numbers with the same base, you add the exponents. So in this case, we add 4 and -2.
3^4 * 3^(-2) = 3^(4 + (-2))
Now we simplify the exponent:
3^4 + (-2) = 3^2
So the expression simplifies to 3^2.
Therefore, the product of 3^4 * 3^(-2) is 3^2.
Your answer of 3^(-8) is incorrect because we should add the exponents, not multiply them. So 3^(-8) is not the correct value.
Instead, the correct answer is 3^2.
I hope this clarifies the correct solution for you.