Simplify the following exponential expression.
120a^4b^2/-24a^9b^-15
is this the right answer
-5a^13b^-17
I will assume you mean
120a^4b^2/(-24a^9b^-15)
if so, then it would be
-5 a^-13 b^17
or
-5b^17/a^13
To simplify the given exponential expression, we can apply the properties of exponents and perform the necessary operations step by step.
Step 1: Simplify the coefficients
The quotient of 120 divided by -24 is -5.
So, the expression becomes:
-5a^4b^2 / a^9b^-15
Step 2: Simplify the variable with the same base, 'a'
When dividing variables with the same base, we subtract their exponents. In this case, we have a^4 divided by a^9, which gives a negative exponent. So we have:
-5 * a^(4 - 9) * b^2 / b^-15
Simplifying further, we get:
-5 * a^(-5) * b^2 / b^-15
Step 3: Simplify variable 'b'
Similar to step 2, when dividing variables with the same base, we subtract their exponents. In this case, we have b^2 divided by b^-15, which gives a positive exponent. So we have:
-5 * a^(-5) * b^(2 - (-15))
Simplifying the exponent, we get:
-5 * a^(-5) * b^(2 + 15)
Finally, combining the exponents:
-5 * a^(-5) * b^17
Hence, the simplified exponential expression is -5a^(-5)b^17.