Simplify the following using positive exponents: .

While there are different ways to approach this problem, we'll go ahead and rewrite the expression so that all exponents are in the numerator. We're doing it this way because the bigger exponent is chilling up top.

Next, since the bases are the same, we can add the exponents together.

x⁶x ^-4 = x²

Simplify the following using positive exponents: .

Once again, there's more than one way to skin a cat, or to simplify exponents. Since we're asked to use positive exponents, it might help to first rewrite the expression using all positive exponents.

We can then use our product rule and add the exponents in the denominator.

Finally, it becomes pretty apparent that the bigger exponent is in the denominator. This means we'll need to bring the x² downstairs by making the exponent negative.

Finally, we can add the exponents for the like bases. Lucky for us, 6 + (-2) = 4 here on planet Earth.

Simplify using only positive exponents: (-3t ^-3)³(-t )⁴t ².

Step numero uno: take care of those darn parentheses. Don't forget to treat that pesky -3 like a regular number, not an exponent.

(-3t ^-3)³(-t )⁴t ² = -27t ^-9t ⁴t ²

Next, we need to add the exponents where bases are the same.

-27t ^-9t ⁴t ² = -27t ^{-9 + 4 + 2} = -27t ^-3

Last but not least, we're asked to use only positive exponents. This means that we need to move our t ^-3 factor to the denominator by changing the sign of its exponent.

Simplify the following using positive exponents: .

Once again, taking care of the parentheses is a great place to start. To do this, we'll raise the whole numbers to the given power and make sure to multiply exponents.

To keep things at a good pace, we'll just take care of our coefficients in this step. That means we need to divide 64 by 16.

Next, since we want positive exponents in our final answer, we'll compare to see where the larger exponents lie. For the a's, it's the numerator; for the b's, the denominator. By changing the signs of the exponents, we can move them up or down to set up our addition in the next step.

Finally, we add exponents with like bases. Keep in mind, we don't typically write the exponent when it's a 1.