Question: Unit Exponents and Polynomials
Progress:
Simplify: $2(f^4)^2 f^2$
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$8f^{12}$
Your answer should contain only positive exponents.
$f^6/4$
$1/6f^2$
$f^4/4$
$1/4f^2$
1. **State the problem:** Simplify the expression $$2(f^4)^2 f^2$$ and express the answer with only positive exponents.
2. **Recall the exponent rules:**
- When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{m \times n}$$
- When multiplying like bases, add the exponents: $$a^m \times a^n = a^{m+n}$$
3. **Apply the power of a power rule:**
$$2(f^4)^2 f^2 = 2 f^{4 \times 2} f^2 = 2 f^8 f^2$$
4. **Apply the multiplication of like bases rule:**
$$2 f^8 f^2 = 2 f^{8+2} = 2 f^{10}$$
5. **Final simplified expression:**
$$2 f^{10}$$
6. **Check answer choices:** None of the provided options match $2 f^{10}$, so the correct simplified form is $2 f^{10}$, which contains only positive exponents.