Question

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


A. 625

B. 1/25

C. 25

D. 5

Answer 1

Answer:

C. 25

Step-by-step 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

Answer 2

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)

$x^1(x^2)=x^{(1+2)}=x^3$

$2^2(2^2)=2^{(2+2)}=2^4=16$

$5^{(\frac{-5}{2} )}*5^{(\frac{9}{2} )}=5^{(\frac{-5+9}{2} )}=5^{(\frac{4}{2} )}=5^2=25$    Your answer is C