Question

simplify. express your answer using exponents.
$(a^{10}b^{-9}c^{-6})^{7}$

Explanation:

Step1: Apply power of a product rule

Distribute the exponent 7 to each term inside the parentheses:
$(a^{10})^7 \cdot (b^{-9})^7 \cdot (c^{-6})^7$

Step2: Apply power of a power rule

Multiply the exponents for each variable:
$a^{10 \times 7} \cdot b^{-9 \times 7} \cdot c^{-6 \times 7}$

Step3: Calculate the new exponents

Compute the product of each exponent pair:
$a^{70} \cdot b^{-63} \cdot c^{-42}$

Answer:

$a^{70}b^{-63}c^{-42}$