Simplifying the Exponent Expression
The problem asks to simplify the expression: $ \frac{225^{0.2} \times 225^{0.3}}{225^{0.6} \times 225^{0.4}} $ We can solve this using the rules of exponents.
Applying Exponent Rules
Recall the exponent rules:
- Product Rule: $a^m \times a^n = a^{m+n}$
- Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$
Step-by-Step Simplification
- Simplify the numerator: Combine the terms using the product rule. $ 225^{0.2} \times 225^{0.3} = 225^{(0.2 + 0.3)} = 225^{0.5} $
- Simplify the denominator: Combine the terms using the product rule. $ 225^{0.6} \times 225^{0.4} = 225^{(0.6 + 0.4)} = 225^{1.0} = 225 $
- Combine numerator and denominator: Use the quotient rule. $ \frac{225^{0.5}}{225^{1.0}} = 225^{(0.5 - 1.0)} = 225^{-0.5} $
- Rewrite the negative exponent: A negative exponent means taking the reciprocal. $ 225^{-0.5} = \frac{1}{225^{0.5}} $
- Evaluate the exponent: $225^{0.5}$ is the square root of 225. $ 225^{0.5} = \sqrt{225} = 15 $
- Final Result: Substitute the value back into the expression. $ \frac{1}{15} $
The simplified value of the expression is $\frac{1}{15}$.
Similar Questions
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- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- Find the value of: $93^{-6} \div 93^{16} \times 93^{-12}$
- The square root of $\frac{(3\frac{1}{4})^{4} - (4\frac{1}{3})^{4}}{(3\frac{1}{4})^{2} - (4\frac{1}{3})^{2}}$ is:
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- Solve the following:
$(625)^{0.17} \times (625)^{0.08} = ?$ - If $\frac{9^m \times 3^5 \times 27^3}{3 \times 81^4} = 3^9$, then the value of m is:
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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 \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
