Exponent Rules 9845F7

1. **Stating the problem:** We need to identify which of the given statements A, B, C, or D is not true. 2. **Recall important exponent rules:** - Any nonzero number raised to the zero power is 1: $a^0 = 1$ - Negative exponents mean reciprocal: $a^{-n} = \frac{1}{a^n}$ - Power of a quotient: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ - Negative exponent on a quotient: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$ 3. **Check each statement:** **A.** $7^0 = 1$ is true by the zero exponent rule. **B.** $4p^{-5} = \frac{1}{4p^5}$ Rewrite left side: $$4p^{-5} = 4 \times p^{-5} = 4 \times \frac{1}{p^5} = \frac{4}{p^5}$$ Right side is: $$\frac{1}{4p^5} = \frac{1}{4 \times p^5}$$ These are not equal because $\frac{4}{p^5} \neq \frac{1}{4p^5}$. So statement B is **not true**. **C.** $\frac{1}{2^8} = 2^{-8}$ is true by the negative exponent rule. **D.** $\left(\frac{m}{n}\right)^3 = \left(\frac{n}{m}\right)^{-3}$ Rewrite right side: $$\left(\frac{n}{m}\right)^{-3} = \left(\frac{m}{n}\right)^3$$ So both sides are equal, statement D is true. 4. **Conclusion:** The only false statement is B. **Final answer:** B is not true.