Sure, let's break down the given expression step by step to understand and simplify it.
1. Expression: [tex]\( 3 a^8 b^{-6} \)[/tex]
2. Handling the negative exponent:
In mathematics, a negative exponent indicates that the base should be moved to the denominator and the exponent should become positive. So, [tex]\( b^{-6} \)[/tex] means [tex]\( \frac{1}{b^6} \)[/tex].
Hence, the expression [tex]\( 3 a^8 b^{-6} \)[/tex] can be rewritten as:
[tex]\[
3 a^8 \cdot \frac{1}{b^6}
\][/tex]
3. Combining the terms:
Multiply the terms together:
[tex]\[
3 \cdot a^8 \cdot \frac{1}{b^6} = \frac{3 a^8}{b^6}
\][/tex]
So, the simplified form of the given expression [tex]\( 3 a^8 b^{-6} \)[/tex] is:
[tex]\[
\frac{3 a^8}{b^6}
\][/tex]
This is the step-by-step solution to the problem!
