Given: \((c^b)^{5}=c^{5+a}\)

Apply the Power of a Power law to the left side to get: \(c^{5b}=c^{5+a}\)

Since the bases are equal, the exponents must be equal: \(5b = 5 + a\)

Subtract \(5\) from both sides to get: \(5b - 5 = a\)

Take Quantity A and replace \(a\) with \(5b - 5\) to get:
QUANTITY A: \(5b - 5\)
QUANTITY B: \(b\)

From here, we can solve the question using a technique called matching operations. See the video below.

Subtract \(b\) from both quantities:
QUANTITY A: \(4b - 5\)
QUANTITY B: \(0\)

Add \(5\) to both quantities:
QUANTITY A: \(4b\)
QUANTITY B: \(5\)

Divide both quantities by \(4\):
QUANTITY A: \(b\)
QUANTITY B: \(1.25\)

Since we are told that \(b\) is an INTEGER greater than 1, quantity A must be greater then quantity B

Answer: A

RELATED VIDEO

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Hi Brent GreenlightTestPrep
silly question that not sure how is 1.25 not greater than 1 here? Thanks Brent

Sir

With all respect I am here to help the students and I suggested you reinforce your fundamental math skills

Now

Manipulating the stem we do have that

5b=5+a

b=5+a/5

or

b=1+a/5

we know that a and b are integers >1

suppose b is 2

2=1+a/5

to have 2 then a must be 5

2=1+5/5=1+1=2

Alike if b=3 a must be 10

3=1+10/5=1+2=3

A > B

A is the answer
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