Determine whether each statement is true or false. If false, corr...

Question

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

Accepted Answer

Hello. Today we're going to be using the properties of exponents to verify that the given statement is true. So what we are given is 17/39 raised to the power of negative eight and that should be equal to 39/17 raised to the power of positive eight. Now, using the power rule for exponents. The power rule states that if you have a quotient A over B to the power of X, you can distribute this exponent to both A. And B. And A over B raised to the power of X. Can be rewritten as eight to the power of X over B to the power of X. So if we apply the power rule to 17/39 race, the power of negative eight, we can go ahead and distribute the negative exponents to both 17 and 39 doing so is going to give us 17 to the power of negative 8/39 to the power of negative eight. And in order to turn these exponents positive, we can go ahead and move 17 to the power of negative eight to the denominator and move 39 to the power of negative eight to the numerator. And doing this is going to give us 39 to the power of positive 8/17 to the power of positive eight. And if we apply the power rule but backwards to 39 to the power of 8/17 to the power of eight. We can rewrite this as 39/17 to the power of eight which matches what's given to us in the original statement. So this proves that the original statement is true. Therefore, the answer to this problem is going to be a So I hope this video helps you in understanding how to approach this problem, and I'll go ahead and see you all in the next video.

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

Key Concepts

Exponents and Negative Exponents

Reciprocal Relationships

Squaring Fractions

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