Simplify the Expression: a⁴/a⁻⁶ Using Exponent Rules

Question

Simplify the following:

a4a6= \frac{a^4}{a^{-6}}=

Video Solution

Solution Steps

00:06 Let's simplify this problem together.
00:10 Remember, when dividing powers with the same base,
00:14 the new power is the difference between the exponents.
00:18 So, we'll subtract the exponents to find the solution.
00:26 And that's how we solve this problem!

Step-by-Step Solution

Since a division operation between two terms with identical bases is required, we will use the power property to divide terms with identical bases:

cmcn=cmn \frac{c^m}{c^n}=c^{m-n} cmcn=cmn \frac{c^m}{c^n}=c^{m-n} Note that using this property is only possible when the division is performed between terms with identical bases.

We return to the problem and apply the power property:

a4a6=a4(6)=a4+6=a10 \frac{a^4}{a^{-6}}=a^{4-(-6)}=a^{4+6}=a^{10} Therefore, the correct answer is option C.

Answer

a10 a^{10}