Which of the following is not equal to $(3^{2})^{3}$ ?

(3^{3})^{2}

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3^{9}

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3^{6}

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3^{3} \times 3^{3}

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Solution

The correct option is B $3^{9}$
According to the law of exponents,

$(a^{m})^{n} = a^{m n}$

$∴ (3^{2})^{3} = 3^{2 \times 3} = 3^{6}$

Also, $(3^{3})^{2} = 3^{2 \times 3} = 3^{6}$

And $3^{3} \times 3^{3} = 3^{3 + 3} = 3^{6}$ $[B e c a u s e a^{m} \times a^{n} = a^{m + n}]$

Since $3^{9} \neq 3^{6}$ , therefore $(3^{2})^{3} \neq 3^{9}$

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Question 1

$[(- 3)^{2}]^{3}$ is equal to
(a) $(- 3)^{8}$
(b) $(- 3)^{6}$
(c) $(- 3)^{5}$
(d) $(- 3)^{23}$

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