What integer values for a and b would make this statement true? 9^(a/b) = 27

Answer 1

Hi

9^(a/b) = 27 is the same as ^b√(9^a) = 27, that is the b^th root of 9^a is equal to 27

With the value of 9, try b = 2 and a = 3 as a starting point.

So 9³ = 9 x 9 x 9 = 729. so then √729 = 27 since 27 x 27 = 729.

CHECK: 9^(3/2) = (3²)^(3/2)...we multiply the exponents so 2 • (³/₂), the 2s cancel out so you have 3³ = 27

Hope this helps

Answer 2

Hi Kyla,

9^(a/b) = 27

log₉9^a/b=log₉27

a/b = log₉27

a/b = log₁₀27/log₁₀9

a/b = 1.5 = 3/2

a = 3

b = 2

Answer 3

9^a/b = 27

9 = 3²

27 = 3³

(3²)^a/b = 3³

3^2a/b = 3³

Since we have the same base (3) on each side of the equal sign, the exponents must be equal:

2a/b = 3

a/b = 3/2

So any combination of a/b = 3/2 works, such as:

a/b = 3/2 = 6/4 = 9/6 = 12/8 = ...