Question

(12x^3)^2×(1/4x^4)^3=(3/2)^2

Answer 1

Ответ:

144x^6×1/64x^12=9/4

9x^6×1/4x^12=9/4

9/4x^18=9/4

x^18=1

x=+-1

x1=-1

x2=1

Объяснение:

x1=-1

x2=1

Answer 2

Let's simplify the expression step by step:

(12x^3)^2 × (1/4x^4)^3 = (144x^6) × (1/64x^12)

To multiply fractions, we multiply the numerators together and the denominators together:

= (144/1) × (x^6/64x^12)

Simplifying the numerator:

= 144/64 × x^6/1 × 1/x^12

= 9/4 × x^(6-12)

= 9/4 × x^(-6)

Now, let's simplify the right side of the equation:

(3/2)^2 = 9/4

Therefore, the simplified expression is:

9/4 × x^(-6) = 9/4

Now we can equate the two sides of the equation:

9/4 × x^(-6) = 9/4

To solve for x, we can cancel out the common terms on both sides by multiplying both sides by 4:

(9/4) × (4) × x^(-6) = (9/4) × (4)

Canceling out the common terms:

9 × x^(-6) = 9

Dividing both sides by 9:

x^(-6) = 1

Since any number raised to the power of -6 is equal to 1 divided by that number raised to the power of 6, we can rewrite the equation as:

1/x^6 = 1

Now, we can solve for x by equating the exponents:

x^6 = 1

Taking the sixth root of both sides:

x = ±1

So, the possible solutions for x are x = 1 or x = -1.