Question

Simplify the following expression. 5^-5/2 * 5^9/2

A. 625

B. 1/25

C. 25

D. 5

Answer 1

When you multiply a base with an exponent by a base with an exponent, you add the exponents together. (But you can only combine the exponents when the bases are the same)

For example:

`(x^3)y^2=x^3y^2` (can't combine the exponents because they have different bases of x and y)

`x^1(x^2)=x^((1+2))=x^3`

`2^2(2^2)=2^((2+2))=2^4=16`

`5^{((-5)/(2) )}*5^{((9)/(2) )}=5^{((-5+9)/(2) )}=5^{((4)/(2) )}=5^2=25` Your answer is C

Answer 2

C. 25

Explanation:

When the numbers with same base are multiplied, their powers add up

5^-5/2 * 5^9/2

5^(-5/2 + 9/2)

5^(4/2)

5^2

25