Properties of Exponents
Using exponent rules to simplify expressions
Properties of Exponents
Using exponent rules to simplify expressions
Math - Grade 6-8
- 1
Simplify: 2^3 x 2^4
Use the product of powers rule.
The expression simplifies to 2^7. When multiplying powers with the same base, add the exponents: 3 + 4 = 7. - 2
Simplify: 5^6 / 5^2
The expression simplifies to 5^4. When dividing powers with the same base, subtract the exponents: 6 - 2 = 4. - 3
Simplify: (3^2)^4
Use the power of a power rule.
The expression simplifies to 3^8. When raising a power to a power, multiply the exponents: 2 x 4 = 8. - 4
Simplify: (2 x 5)^3
The expression simplifies to 2^3 x 5^3, which is 8 x 125 = 1000. When raising a product to a power, apply the exponent to each factor. - 5
Simplify: (12/3)^2
You can simplify the fraction before applying the exponent.
The expression simplifies to 4^2, which equals 16. First simplify inside the parentheses, then square the result. - 6
Write 7 x 7 x 7 x 7 x 7 using exponents.
The expression written using exponents is 7^5. The base is 7 and it is used as a factor 5 times. - 7
Expand 4^3 as repeated multiplication.
The exponent shows the number of equal factors.
The expression 4^3 expands to 4 x 4 x 4. The exponent tells how many times to use the base as a factor. - 8
Simplify: 10^5 x 10^2
The expression simplifies to 10^7. When multiplying powers with the same base, add the exponents: 5 + 2 = 7. - 9
Simplify: 9^4 / 9^1
Use the quotient of powers rule.
The expression simplifies to 9^3. When dividing powers with the same base, subtract the exponents: 4 - 1 = 3. - 10
Simplify: (6^1)^5
The expression simplifies to 6^5. Multiply the exponents: 1 x 5 = 5. - 11
Simplify: (3 x 2)^4
Apply the exponent to both factors inside the parentheses.
The expression simplifies to 3^4 x 2^4, which is 81 x 16 = 1296. A power of a product means each factor gets the exponent. - 12
A square has side length 2^3 units. Write an expression for its area and simplify it.
The area is (2^3)^2, which simplifies to 2^6 or 64 square units. Area of a square is side length times side length. - 13
Simplify: 8^2 / 8^2
Subtract the exponents first.
The expression simplifies to 8^0, which equals 1. Any nonzero number raised to the zero power equals 1. - 14
Simplify: 2^4 x 3^4
The expression simplifies to (2 x 3)^4, which is 6^4 or 1296. When two factors have the same exponent, they can be grouped into one product raised to that exponent. - 15
A bacteria sample doubles every hour. If it starts with 1 cell, write an exponential expression for the number of cells after 6 hours and simplify it.
Start with 1 and multiply by 2 once each hour.
The expression is 2^6, which equals 64. Doubling every hour means multiplying by 2 six times.