Find the numerical equivalent of 3^9. 3^-5 (1 point)
The numerical equivalent of 3^9 * 3^-5 is equal to 3^(9 + (-5)) = 3^4.
To find the numerical equivalent of 3^9 * 3^-5, we can simplify the expression using the laws of exponents.
Using the rule that a^m * a^n = a^(m+n), we can rewrite the expression as:
3^9 * 3^-5 = 3^(9 + -5)
Since adding a negative exponent is the same as subtracting its absolute value, we have:
3^9 * 3^-5 = 3^(9 - 5)
3^(9 - 5) can be further simplified:
3^(9 - 5) = 3^4
Therefore, the numerical equivalent of 3^9 * 3^-5 is 3^4.
To find the numerical equivalent of an expression like 3^9.3^-5, we need to evaluate each exponent separately and then divide the first result by the second result.
Let's start with 3^9. This means we need to multiply 3 by itself 9 times: 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3.
Calculating this multiplication results in 19,683.
Now let's move on to 3^-5. An exponent of -5 indicates that we need to take the reciprocal of the base (in this case, 3) and raise it to the positive exponent (5). So, 3^-5 is equal to 1 / 3^5.
To evaluate 1 / 3^5, we need to raise 3 to the power of 5: 3 * 3 * 3 * 3 * 3.
Calculating this multiplication gives us 243. Taking the reciprocal of 243, we get 1 / 243, which is approximately 0.00411523.
Finally, to find the numerical equivalent of 3^9.3^-5, we divide the result of 3^9 (19,683) by the result of 3^-5 (0.00411523).
19,683 / 0.00411523 ≈ 4,780,287.77.
Therefore, the numerical equivalent of 3^9.3^-5 is approximately 4,780,287.77.