Question

Just How? (2a^2 c^4) ^-5 (c^-1 a^7)^6

Answer 1

Just how? (2a^2 c^4) ^-5 (c^-1 a^7)^6

ANSWER.

$\boldsymbol {(2^2 \ c^4)^{-5} (c^{-1} \ a^7)^6}\\ \\ \boldsymbol {= 2^{-10} \ c^{-20} \ (c^{-1} \ a^7)^6}\\ \\ \boldsymbol {= 2^{-10} \ c^{-20} \ c^{-6} \ a^{42}}\\ \\ \boldsymbol {= 2^{-10} \ a^{42} \ c^{-26}}\\ \\ \boldsymbol {\dfrac{1}{2^{10}} \ a^{42} \ c^{-26}}\\ \\ \boldsymbol {\dfrac{1}{2^{10}} \ a^{42} \ \dfrac{1}{c^{26}}}\\ \\ \\ \boldsymbol {\dfrac{1 \ \cdot \ 1 \ \cdot a^{42}}{2^{10} \ c^{26}}}\\ \\ \\ \boldsymbol {= \dfrac{a^{42}}{1024c^{26}} \ \checkmark.}$ 

$\boldsymbol {\dfrac{a^{42}}{1024c^{26}} \Leftarrow \underline{Answer}}$

REGARDS!

Answer 2

Express with a positive exponent
2∧5 a∧-10 c∧-20 × c∧-6 a∧42
Evaluate the power
1/2∧5×a∧-10 c∧-20 × c∧-6 a∧42
Calculate the product
1/32a∧-10 c∧-20 × c∧-6 a∧42
Express with a positive exponent
1/32a∧32 c∧-26
Calculate the product
1/32a∧32 × 1/c∧26
Answer

a∧32/32c∧26