SaiBook.us Algebra

Home Course Section

Schedule Admission Social

Step-5

Title: Representing Radicals with Exponents

Grade: 8-b Lesson: S2-L1

Explanation: Hello Students, time to practice and review the steps for the problem.

Discussion: Step1 Step2 Step3 Step4 Step5

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Change the following radical expressions to exponential expressions \$root(3)(a^3 b^4)^2\$.
2	Step	Given expression	\$root(3)(a^3 b^4)^2\$
3	Step	Use the property of exponents that allows you to move the exponent of the inside expression outside of the radical:	\$root(3)(a^3 b^4)^2\$ = \$(a^3 b^4)^(2/3)\$
4	Step	Write the final result in exponential notation:	\$(a^3 b^4)^(2/3)\$
5	Step	The radical expression \$root(3)(a^3 b^4)^2\$ is converted to the exponential expression is \$(a^3 b^4)^(2/3)\$.
6	Choice.A	This expression does not match \$root(3)(a^3 b^4)^2\$, which involves a cube root and different base powers	\$(a^3 b^3)^(3/2)\$
7	Choice.B	This option does not match \$root(3)(a^3 b^4)^2\$ because the exponents and bases are different	\$(a^4 b^2)^(3/2)\$
8	Choice.C	This option correctly represents \$root(3)(a^3 b^4)^2\$ in exponential form	\$(a^3 b^4)^(2/3)\$
9	Choice.D	This option has incorrect powers of b and does not match the original expression	\$(a^3 b^2)^(3/2)\$
10	Answer	Option	C
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Change the following radical expressions to exponential expressions \$root(3)(a^3 b^4)^2\$.

Step

Given expression

\$root(3)(a^3 b^4)^2\$

Step

Use the property of exponents that allows you to move the exponent of the inside expression outside of the radical:

\$root(3)(a^3 b^4)^2\$ = \$(a^3 b^4)^(2/3)\$

Step

Write the final result in exponential notation:

\$(a^3 b^4)^(2/3)\$

Step

The radical expression \$root(3)(a^3 b^4)^2\$ is converted to the exponential expression is \$(a^3 b^4)^(2/3)\$.

Choice.A

This expression does not match \$root(3)(a^3 b^4)^2\$, which involves a cube root and different base powers

\$(a^3 b^3)^(3/2)\$

Choice.B

This option does not match \$root(3)(a^3 b^4)^2\$ because the exponents and bases are different

\$(a^4 b^2)^(3/2)\$

Choice.C

This option correctly represents \$root(3)(a^3 b^4)^2\$ in exponential form

\$(a^3 b^4)^(2/3)\$

Choice.D

This option has incorrect powers of b and does not match the original expression

\$(a^3 b^2)^(3/2)\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?

Discussion: Step1 Step2 Step3 Step4 Step5