Question

Решите уравнение (2x^3)^5•(2x^2)^4/(4x^5)^4

Answer 1

$\displaystyle\frac{(2x^{3})^{5} *(2x^{2})^{4}}{(4x^{5})^{4}} = \frac{32x^{15}*16x^{8} }{256x^{20} }=\frac{512x^{23} }{256x^{20} } =2x^{3}$

Answer 2

To solve the equation, let's simplify the expression step by step:

(2x^3)^5 • (2x^2)^4 / (4x^5)^4

Step 1: Apply the exponentiation rules to each term inside the parentheses:

(2^5 * x^(35)) • (2^4 * x^(24)) / (4^4 * x^(5*4))

Step 2: Simplify the exponents:

(32 * x^15) • (16 * x^8) / (256 * x^20)

Step 3: Combine the constants:

(32 * 16 * x^15 * x^8) / (256 * x^20)

Step 4: Further simplify:

(512 * x^(15 + 8)) / (256 * x^20)

Step 5: Simplify the exponents in the numerator:

(512 * x^23) / (256 * x^20)

Step 6: Simplify the constant in the numerator:

(2 * x^23) / (x^20)

Step 7: Use the quotient rule for exponents:

2 * x^(23 - 20)

Step 8: Finalize the solution:

2 * x^3

Therefore, the solution to the equation is 2x^3.