(a) $$ 35,765=3.5765 imes 10^{\mathrm{a}} $$ $$ \mathrm{a}=\square $$

Question

(a) $$ 35,765=3.5765 	imes 10^{\mathrm{a}} $$ $$ \mathrm{a}=\square $$

UpStudy AI · Accepted Answer

1. Write the equation:
   $$
   35\,765 = 3.5765 \times 10^a
   $$

2. Express $$35\,765$$ in scientific notation. To do this, we look for the coefficient $$c$$ such that:
   $$
   35\,765 = c \times 10^n
   $$
   Notice that:
   $$
   35\,765 = 3.5765 \times 10^4
   $$
   because moving the decimal point 4 places to the left yields $$3.5765$$.

3. Compare with the original equation:
   $$
   3.5765 \times 10^a = 3.5765 \times 10^4
   $$

4. Since the coefficients are the same, the exponents must be equal. Thus:
   $$
   a = 4
   $$
$$ a = 4 $$

(a) \( 35,765=3.5765 \times 10^{\mathrm{a}} \) \( \mathrm{a}=\square \)

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