Question

the number 1960 can be written as $1960 = 2^3 \times 5^1 \times a^b$. what is the sum of $a + b$.

Explanation:

Step1: Factorize 1960

First, we know that \(1960 = 2^3\times5^1\times a^b\). Let's factorize 1960. We divide 1960 by \(2^3\times5^1\). \(2^3 = 8\), \(5^1=5\), so \(8\times5 = 40\). Then \(1960\div40=\frac{1960}{40} = 49\).

Step2: Express 49 as a power

We know that \(49 = 7^2\), so \(a = 7\) and \(b = 2\).

Step3: Calculate \(a + b\)

Now we calculate \(a + b\), which is \(7+2=9\).

Answer:

9