# [ASK] find abc if a^2bc^3=5^3 and ab^2=5^6

• MHB
• Monoxdifly
In summary, to solve for abc in the given equation, we can isolate the variable by dividing both sides of the equation by the known values and then plug in the given values for ab^2 and simplify. This equation can have multiple solutions for abc, and to find all possible solutions, algebraic methods such as substitution or elimination can be used. There are various methods and formulas that can be used to solve equations with multiple variables and exponents, and it is important to carefully analyze the given equation to choose the most appropriate method. To check the correctness of the solution for abc, one can substitute the values into the original equation or use a calculator. There are restrictions on the values of a, b, and c in this equation, such
Monoxdifly
MHB
If $$\displaystyle a^2bc^3=5^3$$ and $$\displaystyle ab^2=5^6$$, what does abc equal to? I'm stuck and always getting 0 = 0 or c = c.

Monoxdifly said:
If $$\displaystyle a^2bc^3=5^3$$ and $$\displaystyle ab^2=5^6$$, what does abc equal to? I'm stuck and always getting 0 = 0 or c = c.

I have a feeling that you must have been told \displaystyle \begin{align*} a\,c^2 = 5^6 \end{align*}, not \displaystyle \begin{align*} a\,b^2 \end{align*}. Assuming that I am right...

\displaystyle \begin{align*} a^2\,b\,c^3 &= 5^3 \\ a\,c^2\left( a\,b\,c \right) &= 5^3 \\ a\,b\,c &= \frac{5^3}{a\,c^2} \\ a\,b\,c &= \frac{5^3}{5^6} \\ a\,b\,c &= \frac{1}{5^3} \\ a\,b\,c &= \frac{1}{125} \end{align*}

## 1. How do I solve for abc in the given equation?

To solve for abc, we can start by isolating the variable by dividing both sides of the equation by the known values. This will leave us with the equation abc = 5^9/ab^2. From there, we can plug in the given values for ab^2 and simplify to find the value of abc.

## 2. Can this equation have multiple solutions for abc?

Yes, it is possible for this equation to have multiple solutions for abc. Since the given values of a, b, and c are not specified, there could be more than one combination of values that satisfy the equation. To find all possible solutions, we can use algebraic methods such as substitution or elimination.

## 3. Is there a specific method or formula to solve this type of equation?

Yes, there are various methods and formulas that can be used to solve equations with multiple variables and exponents. Some commonly used methods include substitution, elimination, and factoring. It is important to carefully analyze the given equation and choose the most appropriate method for solving it.

## 4. How can I check if my solution for abc is correct?

To check if your solution for abc is correct, you can substitute the values of a, b, and c into the original equation and see if it satisfies the equation. If the values on both sides of the equation are equal, then your solution is correct. You can also use a calculator to plug in the values and check if the equation holds true.

## 5. Are there any restrictions on the values of a, b, and c in this equation?

Yes, there are certain restrictions on the values of a, b, and c in this equation. Since we are dealing with exponents, the values of a, b, and c must be positive real numbers. Additionally, the value of b cannot be 0 since it appears as a denominator in the equation. It is important to keep these restrictions in mind when solving the equation.

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