An exponent is a number that indicates how many times to multiply the base by itself. For example, in $$2^3$$ , 2 is the base and 3 is the exponent, meaning $$2 \times 2 \times 2 = 8$$ .

A cube root of a number x is a value that, when multiplied by itself three times, gives x. It is denoted as $$\sqrt[3]{x}$$ . For example, $$\sqrt[3]{27} = 3$$ .

What is the value of $$5^{-5} \cdot 5^6$$ ?

Using the property of exponents, $$5^{-5} \cdot 5^6 = 5^{-5+6} = 5^1 = 5$$ .

If a cube has a volume of 64 cubic centimeters, what is the length of one side?

The volume of a cube is given by $$V = s^3$$ , where s is the side length. Therefore, if $$V = 64$$ , then $$s = \sqrt[3]{64} = 4$$ .

What is the simplified form of $$c^4 \cdot c^3$$ ?

Using the product of powers property, $$c^4 \cdot c^3 = c^{4+3} = c^7$$ .

What is the value of $$\frac{(8^2)^3}{8^6}$$ ?

Using the power of a power property, $$\frac{(8^2)^3}{8^6} = \frac{8^{2 \cdot 3}}{8^6} = \frac{8^6}{8^6} = 1$$ .

Which of the following is NOT equivalent to $$12^8$$ ?

The expression $$\left(12^2\right)^6$$ is equivalent to $$12^{12}$$ , which is NOT equal to $$12^8$$ .

What is the value of $$12^3 \cdot 12^5$$ ?

Using the product of powers property, $$12^3 \cdot 12^5 = 12^{3+5} = 12^8$$ .

What is the relationship between square roots and exponents?

The square root of a number can be expressed as an exponent of 1/2. For example, $$\sqrt{x} = x^{1/2}$$ .

What is the relationship between cube roots and exponents?

The cube root of a number can be expressed as an exponent of 1/3. For example, $$\sqrt[3]{x} = x^{1/3}$$ .

What is the value of $$(12^4)^2$$ ?

Using the power of a power property, $$(12^4)^2 = 12^{4 \cdot 2} = 12^8$$ .

Unit 2 Flashcard Review: Exponents, Square Roots and Cube Roots Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponent?

Back

2.

FLASHCARD QUESTION

Front

What is the value of any non-zero number raised to the power of 0?

Back

3.

FLASHCARD QUESTION

Front

What is the product of two powers with the same base?

Back

4.

FLASHCARD QUESTION

Front

What is the quotient of two powers with the same base?

Back

5.

FLASHCARD QUESTION

Front

What is a square root?

Back

6.

FLASHCARD QUESTION

Front

What is a cube root?

Back

7.

FLASHCARD QUESTION

Front

Back

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