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mr Goodwill [35]
3 years ago
13

which of the following is equivalent to (3^x+1)(3^x-1)^2/9^x for all x? a. 3^2x-1 b. 3^x c. 3^x-1 d. 3^x-2 e. 3^3-x

SAT
1 answer:
allsm [11]3 years ago
6 0

Answer:

3^{x-1}

Explanation:

Given

\frac{(3^{x+1})(3^{x-1})^2}{9^x}

Required

Find its equivalent

\frac{(3^{x+1})(3^{x-1})^2}{9^x}

Expand the numerator

\frac{(3^{x+1})(3^{x-1})(3^{x-1})}{9^x}

Apply law of indices: a^m * a^n = a^{m+n}

This gives

\frac{3^{x+1+x-1+x-1}}{9^x}

Collect like terms

\frac{3^{x+x+x+1-1-1}}{9^x}

\frac{3^{3x-1}}{9^x}

Express 9^x as a factor of 3

\frac{3^{3x-1}}{3^2^x}

Apply law of indices: \frac{a^m}{a^n} = a^{m-n}

This gives

3^{3x-1-2x}

3^{3x-2x-1}

3^{x-1}

Hence,

\frac{(3^{x+1})(3^{x-1})^2}{9^x} is equivalent to 3^{x-1}

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