Testinar Grade 7 math

Laws of Exponents

Students will build Grade 7 mastery of laws of exponents using models, equations, and test-style reasoning.

CH04-07 Expressions

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Simplify using the laws of exponents: \(x^3\cdot x^5\)
1. \(x^2\)
2. \(x^8\)
3. \(x^{15}\)
4. \(x^{35}\)
Simplify: \(\frac{a^7}{a^3}\)
1. \(a^{10}\)
2. \(a^4\)
3. \(\frac{a^3}{a^7}\)
4. \(a^{21}\)
Simplify: \((y^2)^6\)
1. \(y^8\)
2. \(y^{12}\)
3. \(y^{36}\)
4. \(2y^6\)
What is the value of \(5^0\)?
1. \(0\)
2. \(1\)
3. \(5\)
4. Undefined
Simplify: \(2^4\cdot 2^2\)
1. \(2^2\)
2. \(2^6\)
3. \(2^8\)
4. \(4^4\)
Simplify: \(f^7\cdot f^2 \cdot f^1\)
1. \(f^9\)
2. \(f^{10}\)
3. \(f^{14}\)
4. \(2f^{10}\)
Simplify: \(\frac{m^5}{m^2}\)
1. \(m^3\)
2. \(m^7\)
3. \(m^{10}\)
4. \(\frac{m}{m^3}\)
What is the value of \((-2)^3\)?
1. \(6\)
2. \(-8\)
3. \(8\)
4. \(9\)

Teacher and parent reference

Answer key and explanations

B. \(x^8\)
When multiplying powers with the same base, add the exponents: \(x^3\cdot x^5=x^{3+5}=x^8\).
B. \(a^4\)
When dividing powers with the same base, subtract the exponents: \(\frac{a^7}{a^3}=a^{7-3}=a^4\).
B. \(y^{12}\)
When raising a power to a power, multiply the exponents: \((y^2)^6=y^{2\times 6}=y^{12}\).
B. \(1\)
Any non-zero number raised to the power of zero equals \(1\): \(5^0=1\).
B. \(2^6\)
Add the exponents when multiplying same bases: \(2^4\cdot 2^2=2^{4+2}=2^6=64\).
B. \(f^{10}\)
Add all exponents: \(f^7 \cdot f^2 \cdot f^1 = f^{7+2+1} = f^{10}\).
A. \(m^3\)
Subtract exponents when dividing: \(\frac{m^5}{m^2}=m^{5-2}=m^3\).
B. \(-8\)
An odd exponent preserves the sign of the base: \((-2)^3=(-2)\cdot(-2)\cdot(-2)=-8\).