Question

Представьте в виде степени выражение: 1) (−x^3 )^5 ⋅ (x^5 ⋅ x^6 )^4;                                                                               2) (x^4)^3*x^2                                                                                 -----------------                                                                                        x^9

Answer 1

(−x³)⁵ ⋅ (x⁵⋅ x⁶)⁴=-x¹⁵x²⁰x²⁴=-x⁵⁹;

(x⁴)³*x² /x⁹=x¹²x²/x⁹=x⁵

Answer 2

1. (−x^3)^5 ⋅ (x^5 ⋅ x^6)^4

First, let's simplify the expressions inside the parentheses: (−x^3)^5 = (−1)^5 ⋅ (x^3)^5 = −x^15

(x^5 ⋅ x^6)^4 = x^(54) ⋅ x^(64) = x^20 ⋅ x^24 = x^44

Now, let's put these simplified expressions back into the original expression: (−x^3)^5 ⋅ (x^5 ⋅ x^6)^4 = (−x^15) ⋅ (x^44)

To find the result when multiplying two expressions with the same base (x in this case) raised to different exponents (−15 and 44), we simply add the exponents: −x^15 ⋅ x^44 = −x^(15+44) = −x^59

So, the expression (−x^3)^5 ⋅ (x^5 ⋅ x^6)^4 is equal to −x^59.

2. (x^4)^3 * x^2

First, let's simplify the expression inside the parentheses: (x^4)^3 = x^(4*3) = x^12

Now, let's put this simplified expression back into the original expression: (x^4)^3 * x^2 = x^12 * x^2

To find the result when multiplying two expressions with the same base (x in this case) raised to different exponents (12 and 2), we simply add the exponents: x^12 * x^2 = x^(12+2) = x^14

So, the expression (x^4)^3 * x^2 is equal to x^14.