Video: Simplifying Algebraic Expressions Using Laws of Exponents

Write 2^(6𝑛) Γ— 3^𝑛 in the form π‘Ž^𝑛.

01:37

Video Transcript

Write two to the sixth 𝑛 power times three to the 𝑛 power in the form π‘Ž to the 𝑛.

In order to do this, we’re going to need to do some rearranging. One of our exponent rules tells us what we can do if we have two different bases that are being taken to the same power. It says π‘₯ to the 𝑛 power times 𝑦 to the 𝑛 power will be equal to π‘₯ times 𝑦 to the 𝑛 power. The problem is one of our exponents is being taken to the sixth 𝑛 power. And the other one is being taken to the 𝑛 power. And we need a form of π‘Ž to the 𝑛 power.

Here, we can use the power to a power rule. If you have π‘₯ to the π‘Ž times 𝑏, that’s the same thing as saying π‘₯ to the π‘Ž power to the 𝑏 power. Two to the sixth 𝑛 power can be rewritten as two to the sixth power to the 𝑛 power. Two to the sixth power to the 𝑛 power times three to the 𝑛 power can be simplified to say two to the sixth power times three to the 𝑛 power. We know that two to the sixth power equals 64. 64 times three equals 192.

The simplified form π‘Ž to the 𝑛 is 192 to the 𝑛 power.

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