Lesson 08: Combining Bases | Unit 7: Exponents and Scientific Notation

Multiple Select

Select **all** the true statements:

• $$2^8 \cdot 2^9 = 2^{17}$$

• $$8^2 \cdot 9^2 = 72^2$$

• $$8^2 \cdot 9^2 = 72^4$$

• $$2^8 \cdot 2^9 = 4^{17}$$

• $$72^3 \cdot 72^2 = 72^5$$

Multiple Select

Select **all** the expressions that have the same value as $$12^4$$ .

• $$(2 \cdot 6)^4$$

• $$6^4 \cdot 2^4$$

• $$3^2 \cdot 4^2$$

• $$12^3 \cdot 12$$

• $$4^4 \cdot 3^4$$

Open Ended

Elena and Diego are evaluating $$(3 \cdot 2)^3$$ . Diego begins by evaluating $$3 \cdot 2$$ , which is 6. His next step is to find $$6^3$$ . Does Diego’s method work? Explain your reasoning.

Open Ended

Elena and Diego are evaluating $$(3 \cdot 2)^3$$ . Elena starts by writing $$(3 \cdot 2)^3 = 3^3 \cdot 2^3$$ . Her next step is to multiply $$3^3$$ by $$2^3$$ . Does Elena’s method work? Explain your reasoning.

Multiple Choice

Which expression has the same value as $$5^3 \cdot 6^3$$ ?

• $$11^6$$

• $$30^6$$

• $$30^3$$

• $$30^9$$

Multiple Select

Select **all** of the expressions that have the same value as $$(3 \cdot 5)^2$$ .

• 4. $$3 \cdot 3 \cdot 5 \cdot 5$$

• 5. $$9 \cdot 25$$

• 3. $$3 \cdot 5 \cdot 3 \cdot 5$$

• 7. 225

• 1. $$15^2$$

Multiple Select

Select **all** the expressions that have the same value as $$4^{10} \cdot 5^{10}$$

• $$9^{10}$$

• $$20^{20}$$

• $$20^{10}$$

• $$2^{10} \cdot 2^{10} \cdot 5^{10}$$

• $$20^{100}$$

Multiple Choice

Rewrite the expression $$(10^2)^{-3}$$ in an equivalent form that uses a single exponent.

• 10^{-6}
• 10^{-9}
• 10^{-3}
• 10^{6}

Multiple Choice

Rewrite the expression $$(3^{-3})^2$$ in an equivalent form that uses a single exponent.

• 3^{-3}
• 3^{-9}
• 3^{0}
• 3^{-6}

Multiple Choice

Rewrite the expression $$3^{-5} \cdot 4^{-5}$$ in an equivalent form that uses a single exponent.

• 12^{5}
• 12^{-5}
• 3^{-5} + 4^{-5}
• (3 \cdot 4)^{-5}