Simplifying expression
I’m starting with the expression \((-1/3)^{-10} \cdot 2x^{-3} \cdot 9^2 \cdot x^5\). It looks like my task here is to simplify this monomial or expression using the laws of exponents. I'm noticing I should check how \(9^2\) and \(x^5\) relate together in this simplification. Let's dig a little deeper into the exponent rules to simplify it correctly!Reassessing mathematical expression
I’m trying to focus on re-rendering the expression, which looks like (-1/3)^{-10} · 2x^{-3} · 9^2 · 25^{-2} · 9?20?. Actually, it could be represented as \(\left(-\frac{1}{3}\right)^{-10}\cdot 2x^{-3}\cdot 9^2\cdot 25^{-2}\cdot 9^{?}20?\). I wonder if I’ve misattributed the 9^2. I should check if there’s a known standard problem related to this and search through my memory of relevant textbook exercises.Simplifying algebraic expressions
I’m looking at the expression involving powers and coefficients, and it feels like an exercise in simplifying by using the base of 3. I remember from previous math tasks that “Упростите выражение” means “simplify the expression.”
So, if I break it down, \((-1/3)^{-10}\) simplifies to \(3^{10}\), and \(9^2\) is \(3^4\). The exponents of \(x\) combine easily, resulting in \(x^2\), leading me to the final simplified answer of \(2 \cdot 3^{14} x^2\). I should just clarify that \(x ≠ 0\) since I’m dealing with negative powers.Seeking clarification in answers
If I’m uncertain about part of the expression, I should mention if the final factor is \(x^5\). The user wants a clear answer, so I could say, "Если выражение на фото: ...". However, the guidance suggests that if it’s not fully readable, I should ask a question instead of making assumptions. I think the image looks readable enough that I should be able to discern the details accurately, so I’ll strive to read it thoroughly.Evaluating a math expression
It seems like I'm looking at an equation to simplify: \((-\frac{1}{3})^{-10}\cdot 2x^{-3}\cdot 9^2\cdot x^5\). The question mark at the far right indicates it's a student’s question, and the expression likely consists of four factors. I think after \(9^2\), there's probably \(x^5\) as a lower-case x, followed by that faint question mark. I’m confirming the expression includes: "(-1/3)^{-10} · 2x^{-3} · 9^2 · x^5."
Краткий ответ: \[ \left(-\frac13\right)^{-10}\cdot 2x^{-3}\cdot 9^2\cdot x^5 =2\cdot3^{14}x^2 =9\,565\,938x^2,\qquad x\ne0. \]
Решение:
Применим правило отрицательной степени: \[ \left(-\frac13\right)^{-10} =\frac{1}{\left(-\frac13\right)^{10}} =3^{10}. \]
Представим \(9^2\) как степень числа \(3\): \[ 9^2=(3^2)^2=3^4. \]
При умножении степеней с одинаковым основанием показатели складываются: \[ x^{-3}\cdot x^5=x^{-3+5}=x^2. \]
Тогда: \[ 3^{10}\cdot2\cdot3^4\cdot x^2 =2\cdot3^{10+4}x^2 =2\cdot3^{14}x^2. \]
Проверка: показатель при \(x\) равен \(-3+5=2\), а числовые степени дают \(10+4=14\). Условие \(x\ne0\) необходимо из-за \(x^{-3}\).