Evaluate each expression. See Example 7. 16^1/4

Question

Accepted Answer

Hey everyone here we are asked to consider the given expression and solve it. So we're given the expression of 2401 raised to the power of 1/4. Now our first step here is going to be to reduce this expression and we can do this by rewriting our base here as a power. So our base here we have 2401 and rewriting it as a power. We see that this value is equivalent to seven to the power of four. So now we can use this simplified term to rewrite our expression here and we have that the quantity of seven to the power of four is raised to the power of 1/4. And now all we have to do to finish up solving here is to recall the power rule for exponents which tells us that when we have a power to a power it is equivalent to multiplying the exponents together. So rewriting this expression with that exponent rule in mind we have seven to the power of four times 1/4. And now we just have to simplify our exponent here. We see that four times 1/4 is just one, one. So we have seven to the power of one which is just equal to seven. And therefore our solution to our given expression is answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time

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Evaluate each expression. See Example 7. 16^1/4

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