Video: Laws of Exponents

Fill in the blank: (−2)⁷ × (−2)⁵ = (−2)^(_).

01:38

Video Transcript

Fill in the blank: Negative two to the seventh power times negative two to the fifth power equals negative two to the power of what.

In this question, we’re asked to find the index or power that negative two in the answer would be raised to. We can start by thinking about what the value of negative two to the seventh power would look like. This would mean that we would have negative two seven times. And all of these would be multiplied together. In the same way, negative two to the fifth power means that we have five negative twos all multiplied together. And our negative two to the seventh power is multiplied by our negative two to the fifth power. So that means our seven negative twos are multiplied by our five negative twos.

So how many negative twos have we got in total now? Well, now, we have 12, which means that we could write this as negative two raised to the power of 12. And so our missing exponent value is 12. We could also have answered this using the exponent rule that 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 plus 𝑏. The value of 𝑥 in the original question would be negative two; our two exponents 𝑎 and 𝑏 are seven and five. So our exponent value at the end is equal to 𝑎 plus 𝑏 which would be seven plus five giving us 12, confirming our original answer.

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