5^9•5^-13 equivalent to? A. 5^4 b. 1/5^4 c. 1/5^22 d. 5^9/5^-13
To simplify the expression 5^9 • 5^-13, we can combine the like terms raised to the same base.
Using the property of exponents that states a^m • a^n = a^(m+n), we can rewrite the expression as:
5^(9 + -13)
Simplifying the exponents, we get:
5^(-4)
Now, when raising a number to a negative exponent, we can reciprocate the base and make the exponent positive. Therefore, 5^(-4) is equivalent to 1/5^4.
So, the answer is:
B. 1/5^4