Question

exponents:quiz
part one: matching properties to expressions
identify the following properties using the expressions in the chart below.
1 product of a power. ____
2 power of a power ____
3 power of a product ____
4 quotient of a power ____
a: $a^{5}\cdot a^{2}$
b: $(x^{2})^{5}$
c: $(3y)^{7}$
d: $\frac{m^{8}}{m^{5}}$

Explanation:

1. Product of a Power: This property applies when multiplying two exponents with the same base, adding the exponents: $a^m \cdot a^n = a^{m+n}$. Expression A matches this.
2. Power of a Power: This property applies when raising an exponent to another power, multiplying the exponents: $(a^m)^n = a^{m \cdot n}$. Expression B matches this.
3. Power of a Product: This property applies when raising a product to a power, distributing the exponent to each factor: $(ab)^n = a^n b^n$. Expression C matches this.
4. Quotient of a Power: This property applies when dividing two exponents with the same base, subtracting the exponents: $\frac{a^m}{a^n} = a^{m-n}$. Expression D matches this.

Answer:

[1] Product of a Power: A. $a^7 \cdot a^2$
[2] Power of a Power: B. $(x^3)^5$
[3] Power of a Product: C. $(3y)^7$
[4] Quotient of a Power: D. $\frac{m^9}{m^2}$