Question

(7x)^9⋅(49x^4)^3:(7x^3)^5⋅(343x)^3⋅x=175 ^-степень. Даю 36 баллов

Answer 1

Ответ на фото/////////////////////

Answer 2

To solve the expression and find the value of x, we need to simplify the given expression first. Let's break down the expression step by step:

(7x)^9⋅(49x^4)^3 : (7x^3)^5⋅(343x)^3⋅x

Step 1: Apply the power of a power rule, which states that (a^b)^c = a^(b*c).

(7x)^9 = 7^9 * x^9 (49x^4)^3 = 49^3 * (x^4)^3 = 49^3 * x^(43) = 49^3 * x^12 (7x^3)^5 = 7^5 * (x^3)^5 = 7^5 * x^(35) = 7^5 * x^15 (343x)^3 = 343^3 * x^3

Step 2: Substitute the simplified expressions back into the main expression:

(7^9 * x^9) * (49^3 * x^12) : (7^5 * x^15) * (343^3 * x^3) * x

Step 3: Use the rule of exponents a^m * a^n = a^(m+n) to combine like terms:

= 7^(9+3) * x^(9+12) : 7^5 * 343^3 * x^(15+3+1) = 7^12 * x^21 : 7^5 * 343^3 * x^19

Step 4: Simplify further using the fact that 343 = 7^3:

= 7^12 * x^21 : 7^5 * (7^3)^3 * x^19 = 7^12 * x^21 : 7^5 * 7^9 * x^19 = 7^(12-5-9) * x^(21-19) = 7^(-2) * x^2 = x^2 / 7^2

Now, the expression is in the form of (x^m / a^n), where m=2 and n=2. To make the expression equal to 175^(-1), we equate it to (175^(-1)):

x^2 / 7^2 = 175^(-1)

Now, solve for x:

175^(-1) = 1/175

x^2 / 7^2 = 1/175

x^2 = 1/175 * 7^2

x^2 = 1/25

x = ±√(1/25)

x = ±1/5

So, the possible values of x are x = 1/5 or x = -1/5.

As you provided the correct answer, you will receive the promised 36 points. Great job!