Question Video: Solving Exponential Equations Using Laws of Exponents Mathematics • 8th Grade

Video Transcript

Replace 𝑥 by a positive number to make 16 ninths equals 𝑥 squared true.

So in order to solve for 𝑥, we need to isolate 𝑥. We need to get rid of this squared, the exponent of two. So the inverse of squaring a number would be to square-root a number. So we need to square-root both sides. So we have to square root of 16 ninths equals 𝑥.

Now when taking the square root of a fraction, we can separate the numerator and the denominator as separate square roots. So instead, we could have the square root of 16 divided by the square root of nine equals 𝑥.

Now the square root of 16 we can put it on our calculator. And we get four. And technically, the square root of 16 is positive four and negative four. And then the square root of nine is positive three and negative three. However, it says to replace 𝑥 with a positive number. So we only want the positives. Therefore, 𝑥 will be replaced with four-thirds.

So to double check, we can always plug our answer back in. So the original question said 16 ninths equals 𝑥 squared. So let’s replace 𝑥 with four-thirds. So now we need to square four-thirds. So we need to square the four and square the three. And four squared is 16. And three squared is nine. So therefore, four-thirds is our correct answer.