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Step-5

Title: Simplify the expression

Grade: 8-a Lesson: S3-L4

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Given that \$ (6^-2 \times 27)/(2^-4 \times 3^-1 ) \$
2	Formula:	By using this formula \$a^(-m)/a^(-n) = a^n/a^m\$	\$ (2^4 \times 3^1 \times27)/6^2 \$
3	Step	After simplification we get	\$ (2^4 \times 3^1 \times27)/((2 \times 3)^2 ) \$
4	Step	After simplification	\$ (2^4 \times 3^1 \times27)/((2 \times 3)^2 ) \$
5	Step	After simplification we get	\$ (2^4 \times 3^1 \times 3^3)/(2^2 \times 3^2 ) \$
6	Formula:	By using this formula \$a^(m+n) = a^m *a^n\$	\$ (2^4 \times 3^(1+3))/(2^2 \times 3^2 )\$
7	Step	After simplification we get	\$ (\cancel(2^4)^2 \times \cancel(3^4)^2)/(\cancel2^2 \times \cancel3^2 ) \$
8	Step	After cancellation we get	\$ 2^2 \times 3^2 \$
9	Step	After simplification we get	\$ 2 \times 2 \times 3 \times 3 \$
10	Step	After multiplication we get	\$ 36 \$
11		Answer	B

Step

Type

Explanation

Answer

Problem

Given that
\$ (6^-2 \times 27)/(2^-4 \times 3^-1 ) \$

Formula:

By using this formula \$a^(-m)/a^(-n) = a^n/a^m\$

\$ (2^4 \times 3^1 \times27)/6^2 \$

Step

After simplification we get

\$ (2^4 \times 3^1 \times27)/((2 \times 3)^2 ) \$

Step

After simplification

\$ (2^4 \times 3^1 \times27)/((2 \times 3)^2 ) \$

Step

After simplification we get

\$ (2^4 \times 3^1 \times 3^3)/(2^2 \times 3^2 ) \$

Formula:

By using this formula \$a^(m+n) = a^m *a^n\$

\$ (2^4 \times 3^(1+3))/(2^2 \times 3^2 )\$

Step

After simplification we get

\$ (\cancel(2^4)^2 \times \cancel(3^4)^2)/(\cancel2^2 \times \cancel3^2 ) \$

Step

After cancellation we get

\$ 2^2 \times 3^2 \$

Step

After simplification we get

\$ 2 \times 2 \times 3 \times 3 \$

Step

After multiplication we get

\$ 36 \$

Answer