The correct option is D 3^10We know that: (a^m)^n=a^m× n ∴ (3^3)^3=3^3× 3=3^9 On susbstituting the value of (3^3)^3 in the above expression we get: (3^3)^3×3=3 ...

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Byju's Answer

Standard XII

Mathematics

Permutation: n Different Things Taken r at a Time

333× 3=?

Question

$(3^{3})^{3} \times 3 = ?$

3^{7}

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3^{8}

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3^{9}

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3^{10}

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Solution

The correct option is D $3^{10}$
We know that:
$(a^{m})^{n} = a^{m \times n}$
$∴ (3^{3})^{3} = 3^{3 \times 3} = 3^{9}$
On susbstituting the value of $(3^{3})^{3}$ in the above expression we get:
$(3^{3})^{3} \times 3 = 3^{9} \times 3^{1} = 3^{9 + 1} = 3^{10}$

$∵ a^{m} \times a^{n} = a^{m + n}$

Suggest Corrections

(33)3×3=?

The correct option is D 310We know that: (am)n=am×n ∴ (33)3=33×3=39 On susbstituting the value of (33)3 in the above expression we get: (33)3×3=39×31=39+1=310 ∵am×an=am+n

$(3^{3})^{3} \times 3 = ?$

The correct option is D $3^{10}$
We know that:
$(a^{m})^{n} = a^{m \times n}$
$∴ (3^{3})^{3} = 3^{3 \times 3} = 3^{9}$
On susbstituting the value of $(3^{3})^{3}$ in the above expression we get:
$(3^{3})^{3} \times 3 = 3^{9} \times 3^{1} = 3^{9 + 1} = 3^{10}$

$∵ a^{m} \times a^{n} = a^{m + n}$