Question

2352 is equal to 2 to the power x into 3 to the power Y into 7 ^ Z

Answer 1

2352 when taken factors we get

          2 x 2 x 2 x 2 x 3 x 7 x 7

  so we get 2^4 x 3^1 x 7^2

Answer 2

As given

→ 2352 = $2^x \times 3^y \times 7^z$ -----(1)

Now, we will factorize 2352.

2352 = 2 ×2 × 2×2 × 3 ×7 × 7

          =  $2^4 \times 3^1 \times 7^2$ --------(2)

Equating (1) and (2), we get

→ $2^x \times 3^y \times 7^z =2^4 \times 3^1 \times 7^2$

→ we get , $2^x = 2^4, 3^y = 3^1 , 7^z = 7^2$

So , if base are same , then their exponents must be same if they are equal.

We get, x=4, y=1,z=2