Question

10^9 ____ (2^3)^3 * (5^3)^2

Answer 1

$\frac{10^9}{2^9*5^6}= \frac{2^9*5^9}{2^9*5^6}=5^{9-6}=5^3=125$

Answer 2

Let's simplify the expression step by step:

1. Simplify the exponents within the parentheses:

   • $(2^3)^3 = 2^{3 \cdot 3} = 2^9$
   • $(5^3)^2 = 5^{3 \cdot 2} = 5^6$

2. Multiply the simplified expressions:

   • $2^9 \times 5^6$

3. Apply the rules of exponents:

   • $a^m \times a^n = a^{m + n}$
   • So, $2^9 \times 5^6 = 2^{9 + 6} \times 5^6 = 2^{15} \times 5^6$

4. Calculate the values:

   • $2^{15} = 32,768$
   • $5^6 = 15,625$

5. Multiply the calculated values:

   • $32,768 \times 15,625 = 511,621,875$

So, $10^9$ is equal to $511,621,875 \times 10^0$, which simplifies to $511,621,875$.