Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}

Question

5
3

1
​
not 5−35^{-3}5
−3
.

y−5⋅y−8⋅y−7=y^{-5}\cdot y^{-8}\cdot y^{-7}=y
−5
⋅y
−8
⋅y
−7
=

Answer 1

To simplify the expression \( y^{-5} \cdot y^{-8} \cdot y^{-7} \), we can use the property of exponents that states when multiplying two powers with the same base, we add their exponents:

\[ y^{-5} \cdot y^{-8} \cdot y^{-7} = y^{-5 + (-8) + (-7)} \]

Now, let's add the exponents:

\[ -5 + (-8) + (-7) = -5 - 8 - 7 = -20 \]

So we have:

\[ y^{-5} \cdot y^{-8} \cdot y^{-7} = y^{-20} \]

To write this in exponential form with positive exponents only, we convert \( y^{-20} \) to:

\[ \frac{1}{y^{20}} \]

Thus, the fully simplified expression is:

\[ \frac{1}{y^{20}} \]