Question

A^9⋅a^(2^(log(a)b^3))

Answer 1

Объяснение:

В зависимости от условия может быть 2 варианта ответа:

$a^{9}*(a^{2)^{\log_{a}{b^{3}}} } = a^{9} * a^{2{\log_{a}{b^{3}}}} = a^{9} * a^{2 * 3{\log_{a}{b}}} = a^{9} * a^{6{\log_{a}{b}}} = a^{9} * (a^{{\log_{a}{b}}})^{6} = a^{9} * b^{6}$

$a^{9}*a^{(2^{\log_{a}{b^{3}}}) } = a^{9} * a^{2^{3\log_{a}{b}}} = a^{9} * a^{8^{\log_{a}{b}}} = a^{9 + 8^{\log_{a}{b}}}$

Answer 2

To simplify the expression A^9 * a^(2^(log(a)b^3)), you can use the properties of exponents and logarithms. Let's break it down step by step:

1. Start with A^9 * a^(2^(log(a)b^3)).

2. Use the property of exponents that says a^(m * n) = (a^m)^n. In this case, m = 9 and n = 2^(log(a)b^3):

   A^9 * (a^(2^(log(a)b^3))) = A^9 * (a^((2^(log(a)b^3))))

3. Now, let's deal with the a^(2^(log(a)b^3)) part. To simplify this, we'll use the properties of logarithms. Recall that a^(log_a(x)) = x. We can use this property to simplify the exponent.

   a^(2^(log(a)b^3)) = a^(log_a(a^(2^(log(a)b^3))))

   Since log_a(a^x) = x, we get:

   a^(2^(log(a)b^3)) = a^(2^(log(a)b^3))

4. Now, the expression becomes:

   A^9 * (a^(2^(log(a)b^3)) = A^9 * (a^(2^(log(a)b^3))

5. We can see that we can't simplify this further without knowing the specific values of A and a.

If you have specific numerical values for A and a, you can calculate the expression. Otherwise, this is the simplified form of the expression.