Simplify 4 to the power of-3 × y to the power of-5 divided by 2 to the power of-5 × 3 to the power of-6 × 9 to the power of-4
Answers
Answer:
Sorry I didn't get a chance to me and I will be in the work
Step-by-step explanation:
Simplify the following expression:
\mathbf{\color{green}{\dfrac{6^8}{6^5}}}
6
5
6
8
The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.
\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}
6⋅6⋅6⋅6⋅6
6⋅6⋅6⋅6⋅6⋅6
How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:
= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=
1
6⋅6⋅6
=6
3
Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.
Simplify the following expression:
\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}
t
8
t
10
How many extra copies of t do I have, and where are they? I have two extra copies, on top:
\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}
t
8
t
10
=
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=
1
t⋅t
=t
2
Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.
make as brainliest