Let r be the result of doubling both the base and the exponent of a^b, b≠0. If r equals the product of a^b by x^b, then x equals:

1961 AMC 12 Problem 9

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Let

r

be the result of doubling both the base and the exponent of

a^b,

b\ne0.

r

equals the product of

a^b

x^b,

then

x

equals:

a

2a

4a

2

4

Write the doubled expression as

(2a)^{2b}

Express both sides as a single quantity raised to the

b

th power

We have

r=(2a)^{2b}=(4a^2)^b

and also

r=a^bx^b=(ax)^b.

Thus

ax=4a^2,

x=4a.

Therefore, the correct answer is C.