Find the product of 2^2⋅2^3 using the Product Rule of Exponents.

Answer 1

The Product Rule of Exponents states that $a^m \cdot a^n=a^{m+n}$. Using this property gives \[2^2\cdot 2^3=2^{2+3}=2^5=\boxed{32}.\]

Answer 2

Using the Quotient Rule of Exponents, what is an equivalent form of 5^4÷5^2 ?

Answer 3

The Quotient Rule of Exponents states that $a^m \div a^n = a^{m-n}$, as long as $a \neq 0$. Using this property gives \[5^4 \div 5^2 = 5^{4-2} = 5^2 = \boxed{25}.\]

Answer 4

Using the Quotient Rule of Exponents, what is an equivalent form of (1/3)^10÷(1/3)^2

Answer 5

We can use the Quotient Rule of Exponents, which states that $a^m \div a^n = a^{m-n}$, as long as $a \neq 0$. Applying this rule gives us \[\left(\frac{1}{3}\right)^{10} \div \left(\frac{1}{3}\right)^2 = \left(\frac{1}{3}\right)^{10-2} = \left(\frac{1}{3}\right)^8.\] Thus, an equivalent form of $(1/3)^{10} \div (1/3)^2$ is $\boxed{\left(\frac{1}{3}\right)^8}$.