The Product Property of Exponents, $x^a \cdot x^b = x^{a+b}$, requires which condition to be true?

The exponents must be the same.

The exponents must be positive.

The expression must have coefficients.

Simplifying and Evaluating Expressions with Integer and Zero Exponents Practice — Grade 9 math

1. Simplify the expression $n^3 \cdot n^8$. The result is ___.
2. Which expression is equivalent to $c^8 \cdot c^{-3}$?
- A. $c^{-24}$
- B. $c^5$
- C. $c^{11}$
- D. $2c^5$
3. Simplify the expression $(6w^2) \cdot (3w^6)$. The result is ___.
4. Simplify the expression $(4m^3n^5) \cdot (5m^4n)$.
- A. $20m^7n^5$
- B. $9m^7n^6$
- C. $20m^{12}n^5$
- D. $20m^7n^6$
5. The Product Property of Exponents, $x^a \cdot x^b = x^{a+b}$, requires which condition to be true?
- A. The exponents must be the same.
- B. The bases must be the same.
- C. The exponents must be positive.
- D. The expression must have coefficients.
6. Which expression is equivalent to $12p^0$, assuming $p$ is not zero?
- A. 12
- B. 1
- C. 0
- D. 12p
7. Simplify the expression $c^{-9}$ by writing it with a positive exponent. The simplified expression is ___.
8. Simplify the expression $\frac{5a^{-3}b^2}{c^{-6}}$ so that all exponents are positive.
- A. $\frac{5b^2c^6}{a^3}$
- B. $\frac{5}{a^3b^2c^6}$
- C. $5a^3b^2c^6$
- D. $\frac{b^2c^6}{5a^3}$
9. Simplify the expression $\frac{1}{k^{-5}}$ by writing it with a positive exponent. The result is ___.
10. First, simplify the expression $18p^2 \cdot p^{-3}$. Then, evaluate the result for $p = 3$. The final value is ___.