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Answer:
[tex]2^{17} \times3^{7}[/tex]
Step-by-step explanation:
Given expression:
[tex](2^9 \times3^5) \times (2^4 \times 3)^2[/tex]
To simplify the given expression, we can use the rules of exponents.
Begin by applying the power of a product rule, which states that when a product is raised to an exponent, each factor in the product is raised to that exponent.
[tex](2^9 \times3^5) \times (2^4)^2 \times (3)^2[/tex]
Now, apply the power of a power rule to (2⁴)², which states that when raising a base with an exponent to another exponent, the exponents are multiplied together:
[tex](2^9 \times3^5) \times 2^{(4 \times 2)} \times (3)^2[/tex]
[tex](2^9 \times3^5) \times 2^{8} \times (3)^2[/tex]
The brackets are unnecessary in this context because the multiplication operation is associative, meaning the order in which we perform the multiplication does not matter. Therefore:
[tex]2^9 \times 3^5 \times 2^{8} \times 3^2[/tex]
Collect like terms:
[tex]2^9 \times 2^{8} \times3^5 \times 3^2[/tex]
Finally, apply the product rule, which states that when multiplying two powers with the same base, add the exponents:
[tex]2^{(9 +8)} \times3^{(5 +2)}[/tex]
[tex]2^{17} \times3^{7}[/tex]
Therefore, the given expression simplifies to:
[tex]\LARGE\boxed{\boxed{2^{17} \times3^{7}}}[/tex]
Answer:
[tex]2^{17}+3^7[/tex]
Formulas:
[tex](n^a)^b=n^{a\cdot b}[/tex]
[tex]n^a\cdot n^b=n^{a+b}[/tex]
Step-by-step explanation:
[tex](2^9 \cdot 3^5) \cdot (2^4\cdot 3)^2 = 2^9\cdot 3^5 \cdot 2^{4\cdot 2} \cdot 3^2 = 2^{9+4\cdot2} \cdot 3^{5+2}=\boxed{\bf 2^{17} + 3^7}[/tex]