If a 0, b = 2a, and c = 2b, which of the following is equivalent to a^b b^c ?

Question

If a > 0, b = 2a, and c = 2b, which of the following is equivalent to a^b b^c ?

GMAT Panda · Accepted Answer

D We first express the given relationships of b and c in terms of a b = 2a c = 2b We substitute these expressions for b and c into a^b b^c a^b b^c = a^2a (2a)^4a We expand (2a)^4a by raising each factor to the power 4a (2a)^4a = 2^4a a^4a We apply Multiplying Exponents of the Same Base to combine a^2a and a^4a a^2a a^4a = a^2a + 4a = a^6a We rewrite 2^4a and a^6a using Exponents of Exponents and combine them 2^4a = (2^4)^a = 16^a a^6a = (a^6)^a 2^4a a^6a = (16 a^6)^a

Explanation	Calculations	Help
$We first express the given relationships of b and c in terms of a$	$b = 2 a c = 2 b$
$We substitute these expressions for b and c into a^{b} b^{c}$	$a^{b} \times b^{c} = a^{2 a} \times (2 a)^{4 a}$
$We expand (2 a)^{4 a} by raising each factor to the power 4 a$	$(2 a)^{4 a} = 2^{4 a} \times a^{4 a}$
$We apply Multiplying Exponents of the Same Base to combine a^{2 a} and a^{4 a}$	$a^{2 a} \times a^{4 a} = a^{2 a + 4 a} = a^{6 a}$
$We rewrite 2^{4 a} and a^{6 a} using Exponents of Exponents and combine them$	$2^{4 a} = (2^{4})^{a} = 1 6^{a} a^{6 a} = (a^{6})^{a} 2^{4 a} \times a^{6 a} = (16 \times a^{6})^{a}$

Question

Options:

Steps

Final Answer

Question

Options:

Steps

Final Answer

Related questions