What is 3^{2log_{3}(2)}*3^{7log_{3}(2)} ?

The solution to 3^{2log_{3}(2)}*3^{7log_{3}(2)} is 512

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simplify 3^{2log_{3}(2)}*3^{7log_{3}(2)}

simplify

3^{2 l o g_{3} (2)} \cdot 3^{7 l o g_{3} (2)}

512

Solution steps

3^{2 l o g_{3} (2)} \cdot 3^{7 l o g_{3} (2)}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{2 l o g_{3} (2)} \cdot 3^{7 l o g_{3} (2)} = 3^{2 l o g_{3} (2) + 7 l o g_{3} (2)}

= 3^{2 l o g_{3} (2) + 7 l o g_{3} (2)}

Add similar elements:

2 lo g_{3} (2) + 7 lo g_{3} (2) = 9 lo g_{3} (2)

= 3^{9 l o g_{3} (2)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (3^{l o g_{3} (2)})^{9}

Apply log rule:

a^{l o g_{a} (b)} = b

3^{l o g_{3} (2)} = 2

= 2^{9}

2^{9} = 512

= 512

(2 x + 3) (x + 2)

(- 2 + 10 i) + (- 5 - 4 i)

2 \cdot 2 x

(8 + 3 i) - (6 - 2 i)

\frac{1}{4} x^{2}

What is 3^{2log_{3}(2)}*3^{7log_{3}(2)} ?
The solution to 3^{2log_{3}(2)}*3^{7log_{3}(2)} is 512