Video: Simplifying Algebraic Expressions Using Laws of Exponents

Bethani Gasparine

Simplify (14𝑥¹⁰ ÷ 7𝑥⁴) + 4𝑥⁶, where 𝑥 ≠ 0.

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Video Transcript

Simplify 14𝑥 to the 10th divided by seven 𝑥 to the fourth plus four 𝑥 to the sixth, where 𝑥 is not equal to zero.

First, we must work inside the parentheses. So we need to divide. So we divide our numbers. 14 divided by seven is two. But now we need to divide like bases with exponents. When dividing with like bases, for example, 𝑥 to the 𝑎 divided by 𝑥 to the 𝑏, we can subtract their exponents. So it’s equal to 𝑥 to the 𝑎 minus 𝑏 power. So we will have two 𝑥 to the 10 minus four power.

So before we add, we need to take 10 minus four, resulting in two 𝑥 to the sixth plus four 𝑥 to the sixth. We have a like basis of 𝑥. And adding with like bases is pretty simple. We simply add the numbers in front. And two plus four is six. And then we keep the like base of 𝑥 to the sixth power. So our final answer is six 𝑥 to the sixth power.

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