$(625)^{0.17} \times (625)^{0.08} = ?$
Solving Exponent Multiplication
The problem asks to solve the expression: $(625)^{0.17} \times (625)^{0.08}$.
We can use the exponent rule for multiplication of powers with the same base: $a^m \times a^n = a^{m+n}$.
Step-by-Step Calculation
- Identify the common base, which is 625.
- Add the exponents: $0.17 + 0.08 = 0.25$.
- Rewrite the expression with the combined exponent: $(625)^{0.25}$.
- Recognize that $625 = 5^4$. Substitute this into the expression: $(5^4)^{0.25}$.
- Apply the power of a power rule: $(a^m)^n = a^{m \times n}$. Calculate $4 \times 0.25$.
- The multiplication $4 \times 0.25$ equals $1$.
- The expression simplifies to $5^1$.
- Calculate the final result: $5^1 = 5$.
Therefore, $(625)^{0.17} \times (625)^{0.08} = 5$.
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Important Questions from Surds and Indices
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