Graduate Management Admission Test (GMAT) Practice Test

How is the expression 25⁷ x 4⁸ converted into the format A x 10^b?

1. 2² x 5¹⁴

2. 5¹⁴ x 2¹⁶

3. 4 x 25⁷

4. 25² x 4²

The correct answer is: 5¹⁴ x 2¹⁶

To convert the expression \( 25^{7} \times 4^{8} \) into the format \( A \times 10^{b} \), it's important to first express 25 and 4 in terms of their prime factors. The number 25 can be expressed as \( 5^2 \). Therefore: \[ 25^7 = (5^2)^7 = 5^{14} \] Similarly, the number 4 can be expressed as \( 2^2 \). Thus: \[ 4^8 = (2^2)^8 = 2^{16} \] Now we can combine these results: \[ 25^{7} \times 4^{8} = 5^{14} \times 2^{16} \] In the product \( 5^{14} \times 2^{16} \), we can reformat this into the form \( A \times 10^{b} \) by recognizing that \( 10 \) can be expressed as \( 2 \times 5 \). Therefore, we can factor a \( 10 \) out of the expression: \[ 5^{14} \times 2^{16} =