Video: Using Laws of Powers to Divide Numbers Raised to Integer Powers in Word Problems

A flea of length 14⁻¹ inches can jump to a height of 14 inches. How many times its length is this?

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Video Transcript

A flea of length 14 to the negative one inches can jump to a height of 14 inches. How many times its length is this?

If we write down an equation, 14 inches equals 14 to the negative one inches times what? We can use a variable 𝑡 here. To solve for 𝑡, we’ll divide by 14 to the negative one on the right side and the left side. 14 to the negative one over 14 to the negative one cancels out, leaving us with 𝑡 equals 14 over 14 to the negative one.

If we break this down, we know that it means 14 divided by 14 to the negative one. We also know that 14 to the negative one equals one over 14. Now, we’re trying to figure out 14 divided by one over 14.

To do this, we change the division symbol to multiplication. And we multiply by the reciprocal. We multiply by 14 over one. 14 times 14 equals 196. Our 𝑡 value, our missing value, is 196.

The flea can jump 196 times its length.

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