Question

(3a^-4 / 2b^-3)^-2 * 10a^7 b^3

Answer 1

Ответ:

Объяснение: помогут свойства степени  после раскрытия скобок получим 4а^8/9b^6 *10a^7 b^3=40a^15/9b^3

Answer 2

To simplify the given expression, we'll start by applying the negative exponent rule, which states that for any non-zero number "a," a^(-n) = 1 / a^n. Let's proceed with the simplification step by step:

Step 1: Apply the negative exponent rule to the expression (3a^(-4) / 2b^(-3))^(-2): (3a^(-4) / 2b^(-3))^(-2) = (2b^(-3) / 3a^(-4))^2

Step 2: Squaring the expression inside the parentheses: (2b^(-3) / 3a^(-4))^2 = (2b^(-3))^2 / (3a^(-4))^2 = (4b^(-6)) / (9a^(-8))

Step 3: Apply the negative exponent rule again to get rid of negative exponents: (4b^(-6)) / (9a^(-8)) = 4b^(6) / 9a^(8)

Now, we have simplified the given expression to (4b^6) / (9a^8).

Step 4: Multiply the simplified expression by 10a^7b^3: (4b^6) / (9a^8) * 10a^7b^3

Step 5: Simplify further by multiplying the coefficients and adding the exponents with the same base: (4 * 10) * (b^6 * b^3) / (9 * a^8 * a^7) = 40 * b^(6 + 3) / 9a^(8 + 7) = 40 * b^9 / 9a^15

Therefore, the final simplified expression is 40b^9 / 9a^15.