maths help again?

Question

If 8^x = 15 and 8^y = 25, then 8^(2x+y) =

(A) 55
(B) 80
(C) 250
(D) 5,625

Can you please explain how you got your answer.. thanks

Answer 1

Remember when you add powers you multiply

8^(2x+y) = 8^x X 8^x X 8^y
=15*15*25
= 5625
= D

Answer 2

Using the rules of indices:

8^(2x + y) = 8^2x * 8^y = (8^x)^2 * 8^y

Since we know 8^x and 8^y we get:

15^2 * 25 = 5625, so d) is your answer.

Answer 3

Whenenver a number with any power is multiplied with the same number with the same or different power, the powers are added.

=>6^(3) * 6^(5)=6^(3+5)=6^(8)

similarly, (8^x)^2=(8^x)*(8^x)=8^(2x)=15*15=225

8^y=25....given

Multiply the two results.

=>(8^(2x)) * 8^y = 8^(2x+y)=225*25=5625


(D)

Answer 4

We know that 8^(2x+y) simplifies to: 8^(2x)*8^y.

We know that 8^y = 25. To find 8^(2x) we just square each side of 8^x = 15. Thus, 8^(2x) = (8^x)^2 = 15^2.

So, your answer is just (15^2)*25.

Answer 5

If 8^x = 15 and 8^y = 25, then 8^(2x+y) =

8^x = 15

x log 8 = log 15

x = 1.3023

8^y = 25

y log 8 = log 25

y = 1.548

We solved for the values of x and y

so

8^(2x+y) = 8^(2*1.3023 + 1.548)

8^(2x+y) = 8^4.1526

8^(2x+y) = 5625.63
.

Answer 6

First, square : 8^x = 15
So : 8^2x = 225.

Multiply this and 8^y :
So,

8^2x * 8 ^y = 225 * 15

therefore :

8^(2x+y) = 5625

Therfore option D