Simplifying Exponents: Division and Multiplication
The problem requires simplifying an expression involving exponents with the same base ($93$). We need to use the rules of exponents for division and multiplication.
Problem Statement
Find the value of the expression:
$93^{-6} \div 93^{16} \times 93^{-12}$
Exponent Rules
Recall the rules for exponents:
- Division: $a^m \div a^n = a^{m-n}$
- Multiplication: $a^m \times a^n = a^{m+n}$
Step 1: Apply Division Rule
First, simplify the division part of the expression ($93^{-6} \div 93^{16}$):
$93^{-6} \div 93^{16} = 93^{-6 - 16} = 93^{-22}$
Step 2: Apply Multiplication Rule
Now, multiply the result from Step 1 by the remaining term ($93^{-12}$):
$93^{-22} \times 93^{-12} = 93^{-22 + (-12)} = 93^{-22 - 12} = 93^{-34}$
Final Answer
The value of the expression $93^{-6} \div 93^{16} \times 93^{-12}$ is $93^{-34}$.
Similar Questions
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Important Questions from Surds and Indices
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
