Question
Find the value of $47^{-8} \div 47^3 \times 47^{-19}$.
The correct answer is
$47^{-30}$
Correct Answer: $47^{-30}$
Step-by-Step Explanation
To solve this, we apply the Laws of Exponents:
Division Law: $a^m \div a^n = a^{(m - n)}$
Multiplication Law: $a^m \times a^n = a^{(m + n)}$
1. Handle the Division First:
$$47^{-8} \div 47^3 = 47^{(-8 - 3)} = 47^{-11}$$
2. Handle the Multiplication Next:
$$47^{-11} \times 47^{-19} = 47^{(-11 + (-19))}$$
$$47^{-11 - 19} = 47^{-30}$$
3. Final Result:
The value is $47^{-30}$.
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Important Questions from Surds and Indices
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- Find the value of $24^{-10} \div 24^{16} \times 24^{-7}$.
Given that $50^{0.92} = x$, $50^{0.26}= y$ and $x^z = y^3$, then the value of z is close to:
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