Write each expression without negative exponents, and evaluate...

Question

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (5t)^-3

Accepted Answer

Hey everyone in this problem by using the rules of exponents were asked to simplify the following expression and eliminate the negative exponents were given four F. To the exponents negative three. Alright so four F. To the exponent negative three. Okay and we want to pay attention. The negative three is going to apply to four and F. Four F is all in brackets. So that exponent applies to that whole expression. Alright so we want to eliminate negative exponents. Let's recall our exponent rule for dealing with negative exponents. We have a. To the exponent negative end. We can write this as one over A. To the exponent N. Okay when we have a negative exponents we can move it down to the denominator. That expression and the exponents gonna become positive. So applying this to our expression and again four F. This entire thing has the exponent negative three. So this is going to become one over four f. to the exponent three. Alright so we've eliminated that negative exponent but we can still simplify a little bit. Okay we have four F. To the exponent three. Let's go ahead and try to simplify or expand that. Now what's your call? If we have multiplication and we have a B to the exponents end we can write this as a. To the exponent end times B. To the exponent. Okay so this is our power rule and applying this to our equation in the denominator we're gonna end up with four cute times F. Cute. Okay we can apply that exponent to each of those terms because they're multiplied together. Alright now we can simplify, we have four. Cute. We know that four cubed is going to be equal to 64 so we get 1/64 F cubed. And that is our simplified expression. So if we look at our answer choices, we see that we have answer choice B. R. Simplified expression is 1/64 F cubed. That's it for this one. Thanks everyone for watching. See you in the next video.

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (5t)^-3

Key Concepts

Negative Exponents

Exponentiation of Products

Evaluating Expressions with Variables

Watch next

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (5t)-3

Key Concepts

Negative Exponents

Exponentiation of Products

Evaluating Expressions with Variables

Watch next

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (5t)^-3