How do you simplify $$(a^m)^{n}$$ ?

To simplify $$(a^m)^{n}$$ , multiply the exponents: $$(a^m)^{n} = a^{m \times n}$$ .

How do you simplify $$x^{\frac{2}{3}} \times x^{\frac{1}{3}}$$ ?

Using the product of powers property, add the exponents: $$x^{\frac{2}{3} + \frac{1}{3}} = x^{1} = x$$ .

How do you simplify $$\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}}$$ ?

Using the quotient of powers property, subtract the exponents: $$\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}} = x^{\frac{5}{2} - \frac{1}{2}} = x^{2}$$ .

What does it mean to have a negative exponent?

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: $$a^{-n} = \frac{1}{a^n}$$ .

How do you simplify $$\frac{1}{x^{-\frac{3}{4}}}$$ ?

Using the definition of negative exponents, this simplifies to $$x^{\frac{3}{4}}$$ .

What is the power of a power property?

The power of a power property states that when raising a power to another power, you multiply the exponents: $$(a^m)^n = a^{m \times n}$$ .

How do you simplify $$\frac{(2x^{\frac{1}{2}})^3}{4}$$ ?

First simplify the numerator: $$(2^3)(x^{\frac{1}{2} \times 3}) = 8x^{\frac{3}{2}}$$ . Then divide by 4: $$\frac{8x^{\frac{3}{2}}}{4} = 2x^{\frac{3}{2}}$$ .

What is the simplified form of $$\frac{25x^2y^3}{75x^{7y^0}}$$ ?

This simplifies to $$\frac{1}{3} \times \frac{y^3}{x^5} = \frac{y^3}{3x^5}$$ .

How do you express $$\frac{y^{12}}{3^4x^{20}}$$ in terms of positive exponents?

This expression already has positive exponents, as both the numerator and denominator are expressed with positive powers.

What is the simplified form of $$\frac{x^2}{x^{\frac{1}{3}}}$$ ?

Using the quotient of powers property, this simplifies to $$x^{2 - \frac{1}{3}} = x^{\frac{6}{3} - \frac{1}{3}} = x^{\frac{5}{3}}$$ .

Simplify Rational Exponents PT

Flashcard

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Mathematics

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9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.A.1, HSA.APR.A.1, HSN.RN.A.2

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FLASHCARD QUESTION

Front

What is a rational exponent?

Back

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CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

Back

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CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the product of powers property?

Back

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CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the power of a product property?

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CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the quotient of powers property?

Back

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CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

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