Question

Plss someone help my do this problem (a^14 • a^-6 / a^25)^3

Answer 1

`a^(-51) = \frac1{a^(51)}`

Explanation:

When you're multiplying two powers with the same base (in our case, a) you add together the exponents.

`((a^1^4\cdot a^-^6)/(a^(25)))^3 =\\(\frac {a^(14+(-5))}{a^2^5})^3= (\frac {a^(14-6)}{a^2^5})^3 = (\frac {a^(8)}{a^2^5})^3`

Now, when you are dividing two powers with the same base (in our case, a again) you subtract the exponents:

`= (a^(8-25))^3 = (a^(-17))^3`

Finally, when you're calculating the power of a power, you multiply the exponents together:

`a^(-17\cdot 3) = a^(-51) = \frac1{a^(51)}`

At this point you just have to choose - or check with your book/teacher if you prefer a negative exponent, or a fraction.