Simplify using the laws of exponents: \(x^3\cdot x^5\)
- A \(x^2\)
- B \(x^8\)
- C \(x^{15}\)
- D \(x^{35}\)
Check answer and explanation
Answer B: \(x^8\)
When multiplying powers with the same base, add the exponents: \(x^3\cdot x^5=x^{3+5}=x^8\).
CH04-07 lesson
Laws of Exponents Learning Activity
A focused Grade 7 learning session for Laws of Exponents using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of laws of exponents using models, equations, and test-style reasoning.
Student goal: I can solve problems involving laws of exponents.
Helpful first:
Rewriting Expressions to Solve Problems
Learn the Idea
Laws of Exponents is part of Grade 7 Expressions. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of laws of exponents using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Laws of Exponents, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving laws of exponents.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsSimplify: \(\frac{a^7}{a^3}\)
- A \(a^{10}\)
- B \(a^4\)
- C \(\frac{a^3}{a^7}\)
- D \(a^{21}\)
Check answer and explanation
Answer B: \(a^4\)
When dividing powers with the same base, subtract the exponents: \(\frac{a^7}{a^3}=a^{7-3}=a^4\).
guided
1 questionSimplify: \((y^2)^6\)
- A \(y^8\)
- B \(y^{12}\)
- C \(y^{36}\)
- D \(2y^6\)
Check answer and explanation
Answer B: \(y^{12}\)
When raising a power to a power, multiply the exponents: \((y^2)^6=y^{2\times 6}=y^{12}\).
practice
5 questionsWhat is the value of \(5^0\)?
- A \(0\)
- B \(1\)
- C \(5\)
- D Undefined
Check answer and explanation
Answer B: \(1\)
Any non-zero number raised to the power of zero equals \(1\): \(5^0=1\).
Simplify: \(2^4\cdot 2^2\)
- A \(2^2\)
- B \(2^6\)
- C \(2^8\)
- D \(4^4\)
Check answer and explanation
Answer B: \(2^6\)
Add the exponents when multiplying same bases: \(2^4\cdot 2^2=2^{4+2}=2^6=64\).
Simplify: \(f^7\cdot f^2 \cdot f^1\)
- A \(f^9\)
- B \(f^{10}\)
- C \(f^{14}\)
- D \(2f^{10}\)
Check answer and explanation
Answer B: \(f^{10}\)
Add all exponents: \(f^7 \cdot f^2 \cdot f^1 = f^{7+2+1} = f^{10}\).
Simplify: \(\frac{m^5}{m^2}\)
- A \(m^3\)
- B \(m^7\)
- C \(m^{10}\)
- D \(\frac{m}{m^3}\)
Check answer and explanation
Answer A: \(m^3\)
Subtract exponents when dividing: \(\frac{m^5}{m^2}=m^{5-2}=m^3\).
Simplify: \((b^3)^4\)
- A \(b^7\)
- B \(b^{12}\)
- C \(b^{81}\)
- D \(b^{64}\)
Check answer and explanation
Answer B: \(b^{12}\)
Multiply exponents when raising a power to a power: \((b^3)^4=b^{3\times 4}=b^{12}\).
exit
3 questionsWhat is the value of \((-2)^3\)?
- A \(6\)
- B \(-8\)
- C \(8\)
- D \(9\)
Check answer and explanation
Answer B: \(-8\)
An odd exponent preserves the sign of the base: \((-2)^3=(-2)\cdot(-2)\cdot(-2)=-8\).
Simplify: \(c^8\div c^5\)
- A \(c^3\)
- B \(c^{13}\)
- C \(c^2\)
- D \(1\)
Check answer and explanation
Answer A: \(c^3\)
Division is subtraction of exponents: \(c^8\div c^5=c^{8-5}=c^3\).
Simplify: \(7^1\)
- A \(0\)
- B \(1\)
- C \(7\)
- D \(49\)
Check answer and explanation
Answer C: \(7\)
Any base to the first power equals itself: \(7^1=7\).
