To simplify the expression [tex]\( c^{-7} \times d^{-7} \)[/tex], we can follow the rules of exponents.
1. Identify the given exponents for both terms:
- The exponent for [tex]\( c \)[/tex] is [tex]\(-7\)[/tex].
- The exponent for [tex]\( d \)[/tex] is [tex]\(-7\)[/tex].
2. Recall the rule for multiplying powers with the same exponent:
- When you multiply two expressions with the same base, you add their exponents. However, in this case, our bases are different but the exponents are the same.
- For two variables [tex]\( c \)[/tex] and [tex]\( d \)[/tex] raised to the same power and then multiplied together, we use the exponent rule: [tex]\( c^a \times d^a = (c \times d)^a \)[/tex].
3. Apply the exponent multiplication rule:
- Given the two variables [tex]\( c \)[/tex] and [tex]\( d \)[/tex] both raised to the power of [tex]\(-7\)[/tex], we can write:
[tex]\[
c^{-7} \times d^{-7} = (c \times d)^{-7}
\][/tex]
4. Simplify the combined exponents:
- The exponent [tex]\(-7\)[/tex] applies to the entire product [tex]\( c \times d \)[/tex].
- We combine the exponents by adding them for the bases [tex]\( c \)[/tex] and [tex]\( d \)[/tex]:
[tex]\[
(c \times d)^{-7 + (-7)} = (c \times d)^{-14}
\][/tex]
Thus, the simplified form of the given expression [tex]\( c^{-7} \times d^{-7} \)[/tex] is:
[tex]\[
(c \times d)^{-14}
\][/tex]
Hence, in a more general form, you could write:
[tex]\[
c^{-7} \times d^{-7} = (c \times d)^{-14}
\][/tex]
