Subjects algebra

Indices Simplification

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Indices Simplification


1. The problem asks to simplify the expression $$8^{-1} \div 8^{2}$$ and leave the answer in terms of indices (exponents). 2. Recall the rule for division of powers with the same base: $$a^{m} \div a^{n} = a^{m-n}$$. 3. Here, the base is 8, and the exponents are $-1$ and $2$. 4. Apply the rule: $$8^{-1} \div 8^{2} = 8^{-1-2}$$. 5. Simplify the exponent: $$-1 - 2 = -3$$. 6. So, the simplified expression is $$8^{-3}$$. 7. This is the answer expressed in indices (exponents).