Learning Rational Exponents

Presentation

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Mathematics

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9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

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

Standards-aligned

Paul Sexton

Used 88+ times

FREE Resource

4 Slides • 21 Questions

Remember, when you have an exponent that is a fraction, its power over root.

Some text here about the topic of discussion.

Rational Exponents

power

root

exponential form

Multiple Choice

Which of the following is correct?

$\frac{Power}{Root}$

$\frac{Root}{Power}$

When simplifying, we must first convert to radical form.

Some text here about the topic of discussion.

Rational Exponents

power

root

exponential form

radical form

We don't write the "2" because it's implied!

Multiple Choice

Which of the following is in radical form?

$\sqrt[4]{5^3}$

$5^{\frac{3}{2}}$

Multiple Choice

Which of the following is in exponential form?

$\sqrt[4]{8^{ }}$

$8^{\frac{1}{4}}$

Multiple Choice

Write the following expression in radical form: $27^{\frac{2}{3}}$

$\sqrt[2]{27^3}$

$\sqrt[]{27^3}$

$\sqrt[3]{27^2}$

$\sqrt[]{27^2}$

Multiple Choice

Write the following expression in radical form: $4^{\frac{5}{2}}$

$\sqrt[]{4^5}$

$\sqrt[5]{4^2}$

$\sqrt[5]{4}$

Multiple Choice

Write the following expression in radical form: $81^{\frac{1}{2}}$

$\sqrt[]{81}$

$\sqrt[]{81^2}$

$\sqrt[1]{81^2}$

$81^2$

Multiple Choice

Write the following expression in radical form: $64^{\frac{1}{3}}$

$\sqrt[]{64^3}$

$\sqrt[1]{64^3}$

$\sqrt[3]{64}$

Match

Match each expression to it's radical form:

$\sqrt[]{25^5}$

$\sqrt[5]{25^2}$

$\sqrt[]{5^{25}}$

$\sqrt[25]{5^2}$

$25^{\frac{5}{2}}$

$25^{\frac{2}{5}}$

$5^{\frac{25}{2}}$

$5^{\frac{2}{25}}$

For example:

Some text here about the topic of discussion.

When simplifying an expression with a rational exponent, take the root first!

-Take the 5th root of 32 first

-Now take the 2nd power

Multiple Choice

When simplifying an expression with a rational exponent, first we ...

take the root

take the power

Multiple Choice

Which of the following orders is correct when simplifying expressions with rational exponents?

Take the root, then the power.

Take the power, then the root.

Multiple Choice

Which of the following steps would you take when simplifying the expression $\sqrt[]{25^3}$

Raise 25 to the 3rd power, then take the square root.

Take the square root of 25, then raise it to the 3rd power.

Fill in the Blanks

Simplify the following expression: $\sqrt[]{25^3}$

Fill in the Blanks

Simplify the following expression: $\sqrt[3]{27^2}$

Fill in the Blanks

Simplify the following expression: $\sqrt[4]{16^3}$

Fill in the Blanks

Simplify the following expression: $\sqrt[]{16^3}$

Fill in the Blanks

Simplify the following expression: $\sqrt[4]{81^3}$

Fill in the Blanks

Simplify the following expression: $\sqrt[3]{8^2}$

Match

Match the following:

$\sqrt[3]{8^4}$

$\sqrt[4]{16^2}$

$\sqrt[]{16^3}$

$\sqrt[4]{81^2}$

$\sqrt[3]{27^4}$

For example:

Some text here about the topic of discussion.

If the expression is written in exponential form, convert it to radical form in order to simplify it.

exponential form

radical form

2.) Take the "root"

1.) Write in radical form

3.) Take the "power"

Reorder

Reorder in the order when simplifying $8^{\frac{2}{3}}$ :

$8^{\frac{2}{3}}$

$=\sqrt[3]{8^2}$

$=2^2$

$=4$

Multiple Choice

Simplify: $8^{\frac{4}{3}}$

Multiple Choice

Simplify: $16^{\frac{1}{2}}$

Remember, when you have an exponent that is a fraction, its power over root.

Some text here about the topic of discussion.

Rational Exponents

power

root

exponential form

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