Determine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m^1/3) = m^2/9

Question

Accepted Answer

Hey everyone here we are asked to use the rules of exponents to identify if the given statement is true or false and if the statement is false we need to modify the right side of the equation to make the equation correct. So our given statement here we have the quantity of X to the power of 1/9 times the quantity of X to the power of 5/9. And we are told that this expression is it equivalent to X to the power of five? Divided by 81. So now to determine if this statement is true we need to just simplify the left hand side of our expression like we normally would. So we have the quantity of X to the power of 1/9 times the quantity of X to the power of five nines. And so to simplify this expression we just need to recall the product rule for exponents which tells us that A to the power of M times A. To the power of N is equivalent to A to the power of M plus N. So now here since we are multiplying terms or multiplying exponents here with the same base we know we can just add the exponents. So our expression becomes X to the power of 1/9 plus five nights. And now we just need to simplify our exponents here. So we have X to the power of 1/9 plus five nights gives us X to the power of 6/9. And then we see that the numerator and the denominator have a common factor of three. So our exponents reduces to two thirds. So we really have X to the power of two thirds. And so now we just need to compare our expression we found to the right hand side of our given statement. And we see that X to the power of two thirds is not equal to the right hand side where we had X to the power of five divided by 81. Therefore we know that our given statement is false. So now our last step is to just rewrite our given statement as its true statement. So doing this, we see our expression where we had the quantity of X to the power of 1/9 times. The quantity of X to the power of 5/9 is actually equal to X to the power of two thirds. And with this we have found our true statement and determined that our original statement was in fact false. And therefore we are left with answer choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Determine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m^1/3) = m^2/9

Verified Solution

Key Concepts

Exponents and Their Properties

Simplifying Expressions

True or False Statements in Algebra