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 $$2 \times 2 \times 2$$ .

Simplify: $$(3^2 \cdot 3^4)$$

Using the product of powers rule, $$3^2 \cdot 3^4 = 3^{2+4} = 3^6$$ .

Simplify: $$(x^3)^2$$

Using the power of a power rule, $$(x^3)^2 = x^{3 \cdot 2} = x^6$$ .

Simplify: $$\frac{5^7}{5^3}$$

Using the quotient of powers rule, $$\frac{5^7}{5^3} = 5^{7-3} = 5^4$$ .

What is $$\sqrt{a^2}$$ ?

The square root of a squared term is the absolute value of the base. Thus, $$\sqrt{a^2} = |a|$$ .

Simplify: $$(-2)^3 \cdot (-2)^6$$

Using the product of powers rule, $$(-2)^3 \cdot (-2)^6 = (-2)^{3+6} = (-2)^9$$ .

What is $$\sqrt{24}$$ ?

To simplify, factor 24 into 4 and 6: $$\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}$$ .

What is $$\sqrt{50}$$ ?

To simplify, factor 50 into 25 and 2: $$\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$$ .

What is $$\sqrt[4]{m^3}$$ ?

Using the power of a root rule, $$\sqrt[4]{m^3} = m^{3/4}$$ .

Exponents RULE! (exponent rules)

Flashcard

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Mathematics

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7th - 12th Grade

•

Practice Problem

•

Medium

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CCSS

8.EE.A.1, 6.EE.A.1, HSN.RN.A.2

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FLASHCARD QUESTION

Front

What is an exponent?

Back

Tags

CCSS.6.EE.A.1

FLASHCARD QUESTION

Front

What is the product of powers rule?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the power of a power rule?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the power of a product rule?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the quotient of powers rule?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the zero exponent rule?

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the negative exponent rule?

Back

Tags

CCSS.8.EE.A.1

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