Question

calculate
\\(\left(5 \times 10^{7}\
ight)^{-2}\\)
write your answer in scientific notation.

Explanation:

Step1: Apply exponent rule to product

$(ab)^n = a^n b^n$
So, $(5 \times 10^7)^{-2} = 5^{-2} \times (10^7)^{-2}$

Step2: Compute base 5 term

$a^{-n} = \frac{1}{a^n}$
$5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04$

Step3: Compute power of 10 term

$(a^m)^n = a^{m \times n}$
$(10^7)^{-2} = 10^{7 \times (-2)} = 10^{-14}$

Step4: Multiply results and adjust

$0.04 \times 10^{-14} = 4 \times 10^{-2} \times 10^{-14}$
Combine exponents: $10^{-2 + (-14)} = 10^{-16}$

Answer:

$4 \times 10^{-16}$