Question

Please help me with these questions

Answer 1

Problem 5)

The bases are the same, so we add the exponents when multiplying something like this out. We have -5+7 = 2 as the final exponent meaning that 5^2 = 25

Answer: Choice B) 25

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Problem 6)

We can multiply the exponents (t^8)^2 = t^(8*2) = t^16

Or we can expand out (t^8)^2 to get (t^8)*(t^8), then add the exponents from here to get t^(8+8) = t^16. Either way we get the same answer

Answer: Choice C) t^16

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Problem 7)

The negative exponent indicates we will apply the reciprocal to get that exponent to a positive number. The rule is x^(-k) = 1/(x^k)

So 5^(-4) = 1/(5^4) = 1/625 and (t^3)^(-4) = t^(3*(-4)) = t^(-12) = 1/(t^12)

Put together, we end up with 1/(625t^12)

Answer: Choice C) 1 over 625t^12