How to simplify.......

[ (16a^-8 b^6 c^2) / (49a^6 b^-2 c^0) ]^ -3/2

[16a^-8b^6c^2 / 49a^6b^-2c^0] ^ -3/2

law of exponents; to the power of 0, it's just 1

[16a^-8b^6c^2 / 49a^6b^-2(1)] ^ -3/2

[16a^-8b^6c^2 / 49a^6b^-2] ^ -3/2

law of exponents; divide the bases, subtract the exponents

[(16/49) times a^(-8-6) times b^(6-(-2)) times c^2] ^ -3/2

[(16/49) times a^-14 times b^8 times c^2] ^ -3/2

law of exponents; to the power of a negative, flip fraction and make power positive

[16/49 times (1/a)^14 times b^8c^2] ^ -3/2

[16/49 times 1/a^14 times (b^8c^2)/1] ^ -3/2

[(16)(1)(b^8c^2) / (49)(a^14)(1)] ^ -3/2

[16b^8c^2 / 49a^14] ^ -3/2

law of exponents; to the power of a negative, flip fraction and make power positive

[49a^14 / 16b^8c^2] ^ 3/2

law of exponents; fractions; numerator is the number of times the quantity mulitplies itself by, denominator is the nth root the quantity is taken by

√[49a^14 / 16b^8c^2]^3

√[49a^14 / 16b^8c^2]^2 times √[49a^14 / 16b^8c^2]^1

[49a^14 / 16b^8c^2]^ (2/2) times √(49a^14 / 16b^8c^2)

(49a^14 / 16b^8c^2) times (√49 times √a^14)/(√16 times √b^8c^2)

(49a^14 / 16b^8c^2) times (7a^7 / 4b^4c)

(49a^14)(7a^7) / (16b^8c^2)(4b^4c)

law of exponents; multiply the bases, add the exponents

7^3a^21 / 4^3b^12c^3

Bring the outer exponent in to each factor:

(16^(-3/2)(a^(-12)b^(-9)c^(-3))/(49^(-3/…

then calculate the constants: 16^(-3/2) = 1/sqrt(16^3) = 1/64
49^(-3/2) = 1/sqrt(49^3) = 1/343

Then you have 343/64 (a^-12/a^-9)(b^-9/b^3)(c^-3/c^0)
Subtract exponents on like bases: 343/64 (a^-3)(b^-12)(c^-3)
The negative exponents go in the denominator

343/(64a^3 b^12 c^3)

O_O!