Question

simplify X to the power of 9 divided by X to the power of 5

Answer 1

Question :

simplify X to the power of 9 divided by X to the power of 5

Answer :

$\frac{ {x}^{9} }{ {x}^{5} } = {x}^{9 - 5} = {x}^{4}$

Hope it helps

Answer 2

The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:

a6 × a5 = (a6)(a5)

= (aaaaaa)(aaaaa)

= aaaaaaaaaaa

= a11

Thus:

a6 × a5 = a11

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.

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