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Step-1

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 \$ (3^-3 \times 10^-3 \times 25)/(5^-4 \times 6^-3 ) \$
2	Step	After simplification we get	\$ (3^-3 \times (5\times2)^-3 \times 25)/(5^-4 \times (2 \times 3)^-3 ) \$
3	Step	After simplification we get	\$ (\cancel(3^-3) \times 5^-3\times \cancel(2^-3) \times 5^2)/(5^-4 \times \cancel(2^-3) \times \cancel(3^-3) ) \$
4	Step	After cancellation we get	\$ (5^-3 \times 5^2)/(5^-4) \$
5	Formula:	By using this formula \$a^(m+n) = a^m *a^n\$	\$ 5^(-3+2)/5^-4 \$
6	Step	After adding we get	\$ 5^-1/5^-4\$
7	Formula:	By using this formula \$a^(-m)/a^(-n) = a^n/a^m\$	\$ \cancel(5^4)^3/\cancel5 \$
8	Step	After cancellation we get	\$ 5^3 = 5 \times 5 \times 5\$
9	Step	After simplification	\$ 125\$
10		Answer	A

Step

Type

Explanation

Answer

Problem

Given that
\$ (3^-3 \times 10^-3 \times 25)/(5^-4 \times 6^-3 ) \$

Step

After simplification we get

\$ (3^-3 \times (5\times2)^-3 \times 25)/(5^-4 \times (2 \times 3)^-3 ) \$

Step

After simplification we get

\$ (\cancel(3^-3) \times 5^-3\times \cancel(2^-3) \times 5^2)/(5^-4 \times \cancel(2^-3) \times \cancel(3^-3) ) \$

Step

After cancellation we get

\$ (5^-3 \times 5^2)/(5^-4) \$

Formula:

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

\$ 5^(-3+2)/5^-4 \$

Step

After adding we get

\$ 5^-1/5^-4\$

Formula:

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

\$ \cancel(5^4)^3/\cancel5 \$

Step

After cancellation we get

\$ 5^3 = 5 \times 5 \times 5\$

Step

After simplification

\$ 125\$

Answer