Question

Which value is equivalent to (8x4x2/8x7)^2x(8^0/7^-3)^3x7^-9?

A. 64/49
B. 8/49
C. 16/7
D. 512/7

Answer 1

To simplify the expression (8x4x2/8x7)^2x(8^0/7^-3)^3x7^-9, follow the steps: simplify each fraction and exponent, substitute the simplified values back into the expression, simplify the exponents, combine the fractions, and multiply the resulting fractions. The equivalent value is 512/7.

Step-by-step explanation:

To simplify the expression (8x4x2/8x7)^2x(8^0/7^-3)^3x7^-9,

1. Simplify each fraction and exponent individually: 8x4x2/8x7 equals 4/7, 8^0 equals 1, and 7^-3 equals 1/343.
2. Substitute the simplified values back into the expression: (4/7)^2x(1/343)^3x7^-9.
3. Simplify the exponents: (4/7)^2 equals 16/49, (1/343)^3 equals 1/343^3, and 7^-9 equals 1/7^9.
4. Combine the fractions: 1/343^3 equals 1/41816151.
5. Multiply the resulting fractions: (16/49) x (1/41816151) equals 16/(49 x 41816151).

The final simplified expression is 16/(49 x 41816151), which is equivalent to option D: 512/7.