Question

(-х³)⁶×(-х⁶)³÷(-х³×х⁴)⁵​

Answer 1

Ответ:

-x

Объяснение:

${( - {x}^{3})}^{6} {( - {x}^{6})}^{3} \div {( - {x}^{3} {x}^{4} )}^{5} = \\ = \frac{ {x}^{3 \times 6}{x}^{3 \times 6} }{ -{({x}^{3 + 4})}^{5} } = \\ = - \frac{ {x}^{18 + 18} }{ {x}^{7 \times 5} } = - \frac{ {x}^{36} }{ {x}^{35} } = - {x}^{36 - 35} = - x$

Answer 2

To simplify the expression (-x³)⁶ × (-x⁶)³ ÷ (-x³ × x⁴)⁵, we can apply the rules of exponents and simplify each term separately.

Let's start with (-x³)⁶. When a negative number is raised to an even power, the result is positive. Therefore, (-x³)⁶ simplifies to (x³)⁶, which is x³⁶.

Next, let's simplify (-x⁶)³. Here, the negative sign is raised to an odd power, so the result remains negative. (-x⁶)³ simplifies to -(x⁶)³, which is -x¹⁸.

Moving on to (-x³ × x⁴)⁵, we can simplify the product inside the parentheses. Multiplying -x³ and x⁴ gives us -x⁷. Now we have (-x⁷)⁵.

Finally, we can simplify the expression by dividing the results obtained above:

(x³⁶) × (-x¹⁸) ÷ (-x⁷)⁵.

Dividing by a negative number is equivalent to multiplying by its reciprocal, so (-x⁷)⁵ becomes (-1/x⁷)⁵, which is (-1)⁵/x³⁵ or -1/x³⁵.

Now we have:

(x³⁶) × (-x¹⁸) ÷ (-1/x³⁵).

To multiply two terms with the same base, we add their exponents. Therefore, (x³⁶) × (-x¹⁸) is equal to x^(36-18) or x¹⁸.

Substituting this back into the expression, we get:

x¹⁸ ÷ (-1/x³⁵).

Dividing by a fraction is equivalent to multiplying by its reciprocal, so (-1/x³⁵) becomes -x³⁵.

The simplified expression is:

x¹⁸ × (-x³⁵) or -x^(18+35) which can be written as -x⁵³.

Therefore, (-x³)⁶ × (-x⁶)³ ÷ (-x³ × x⁴)⁵ simplifies to -x⁵³.