Solve for x in 16x^(-3) = 2x^(-6)?
Well, solving equations can be quite the balancing act. Let's see if we can clown around with these exponents!
So, we have 16x^(-3) = 2x^(-6). To make things a bit easier, let's rewrite it as 16/x^3 = 2/x^6.
To solve this equation, we can cross-multiply to get rid of the fractions. We get 16 * x^6 = 2 * x^3.
Now, divide both sides by 2 to get 8 * x^6 = x^3.
Now, let's pull out our clown tricks and bring both sides to the same power. Taking the cube root of both sides will eliminate the x^6 on the left side, leaving us with 2 * x^2 = x.
To make this a bit more fun, let's rearrange it to get x - 2 * x^2 = 0.
Now, we can factor out an x: x(1 - 2 * x) = 0.
This equation gives us two possible solutions: x = 0 or (1 - 2 * x) = 0.
If we solve the second equation, we get 1 - 2 * x = 0, which gives us x = 1/2.
So, the solutions to the equation 16x^(-3) = 2x^(-6) are x = 0 and x = 1/2.
Now, wasn't that a juggling act? Keep those math problems coming, and I'll keep bringing the laughs!
To solve for x in the equation 16x^(-3) = 2x^(-6), we can start by expressing both sides with the same base and then equating the exponents.
The equation can be rewritten in the form:
16/x^3 = 2/x^6
Now, let's clear the fraction by cross multiplying:
16 * x^6 = 2 * x^3
Next, we simplify the equation by combining like terms:
16x^6 = 2x^3
To isolate x, we can divide both sides of the equation by 2x^3:
16x^6 / (2x^3) = 2x^3 / (2x^3)
This simplifies to:
8x^3 = 1
To solve for x, we can take the cube root of both sides:
(8x^3)^(1/3) = 1^(1/3)
On the left side, the cube root of the cube cancels out, leaving just x:
x = 1^(1/3)
Finally, since the cube root of 1 is 1, the solution is:
x = 1
To solve for x in the equation 16x^(-3) = 2x^(-6), we can start by simplifying the equation by canceling out the common factors.
Step 1: Rewrite the equation using positive exponents:
16 / x^3 = 2 / x^6
Step 2: Cross-multiply:
16 * x^6 = 2 * x^3
Step 3: Simplify:
16x^6 = 2x^3
Step 4: Divide both sides of the equation by 2x^3 to isolate x^3:
16x^6 / 2x^3 = 2x^3 / 2x^3
Step 5: Simplify and cancel:
8x^3 = 1
Step 6: Divide both sides of the equation by 8 to solve for x^3:
8x^3 / 8 = 1 / 8
Step 7: Simplify:
x^3 = 1 / 8
Step 8: Take the cube root of both sides of the equation to solve for x:
∛(x^3) = ∛(1 / 8)
Step 9: Simplify:
x = 1 / ∛8
Step 10: Further simplify the expression:
x = 1 / 2
Therefore, the value of x in the equation 16x^(-3) = 2x^(-6) is x = 1/2.
6x^(-3) = 2x^(-6)
6/x^3 = 3/x^6
6x^6 = 3x^3
2x^6 - x^3 = 0
x^3(2x^3 - 1) = 0
take it from there