Answer:
[tex]a^{-51} = \frac1{a^{51}}[/tex]
Step-by-step explanation:
When you're multiplying two powers with the same base (in our case, a) you add together the exponents.
[tex](\frac{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[/tex]
Now, when you are dividing two powers with the same base (in our case, a again) you subtract the exponents:
[tex]= (a^{8-25})^3 = (a^{-17})^3[/tex]
Finally, when you're calculating the power of a power, you multiply the exponents together:
[tex]a^{-17\cdot 3} = a^{-51} = \frac1{a^{51}}[/tex]
At this point you just have to choose - or check with your book/teacher if you prefer a negative exponent, or a fraction.
