If the expression is in exponential form, write it in radical for...

Question

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -3 √5p³

Accepted Answer

Hello everyone. We're going to convert a radical expression into exponential form. The expression we're given is negative five times the square root of two V. Two. The third since two V. Two the third is in parentheses. I know that whole thing is under my radical. For now I'm gonna leave negative five out front and I'm going to deal with what's in the radical. I'm going to rewrite that in parentheses and I want to make sure I have an exponent. So the square as an exponent is the exponent of one half. So I've rewritten it without a radical with the one half. Now if you notice we don't have any answers that give us an option like this which means they want us to simplify it so that our five is also in our parentheses. To do that. You need to recall that five Squared to the one half is the same thing as five. Well five squared is 25. So 25 to the one half is the same as five. So we're gonna multiply into our parentheses. 25 to the one half. So the negative staying out front, I'm gonna just treat it as a negative one for right now. So it saves the space I have 25 to the one half times two V. Two the third to the one half because they have the same exponents. I can combine what's underneath. So -1 stays out front. 25 times two is 50 V. To the third to the one half. And now I can drop the one and just keep the negative. So I get negative in parentheses 50 V. Two the third to the one half, and that is answer choice B. Have a good day.

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If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -3 √5p³