Properties of Exponents Worksheet

Question 1

Simplify: 2^3 x 2^4

Accepted Answer

The expression simplifies to 2^7. When multiplying powers with the same base, add the exponents: 3 + 4 = 7.

Question 2

Simplify: 5^6 / 5^2

Accepted Answer

The expression simplifies to 5^4. When dividing powers with the same base, subtract the exponents: 6 - 2 = 4.

Question 3

Simplify: (3^2)^4

Accepted Answer

The expression simplifies to 3^8. When raising a power to a power, multiply the exponents: 2 x 4 = 8.

Question 4

Simplify: (2 x 5)^3

Accepted Answer

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.

Question 5

Simplify: (12/3)^2

Accepted Answer

The expression simplifies to 4^2, which equals 16. First simplify inside the parentheses, then square the result.

Question 6

Write 7 x 7 x 7 x 7 x 7 using exponents.

Accepted Answer

The expression written using exponents is 7^5. The base is 7 and it is used as a factor 5 times.

Question 7

Expand 4^3 as repeated multiplication.

Accepted Answer

The expression 4^3 expands to 4 x 4 x 4. The exponent tells how many times to use the base as a factor.

Question 8

Simplify: 10^5 x 10^2

Accepted Answer

The expression simplifies to 10^7. When multiplying powers with the same base, add the exponents: 5 + 2 = 7.

Question 9

Simplify: 9^4 / 9^1

Accepted Answer

The expression simplifies to 9^3. When dividing powers with the same base, subtract the exponents: 4 - 1 = 3.

Question 10

Simplify: (6^1)^5

Accepted Answer

The expression simplifies to 6^5. Multiply the exponents: 1 x 5 = 5.

Question 11

Simplify: (3 x 2)^4

Accepted Answer

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.

Question 12

A square has side length 2^3 units. Write an expression for its area and simplify it.

Accepted Answer

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.

Question 13

Simplify: 8^2 / 8^2

Accepted Answer

The expression simplifies to 8^0, which equals 1. Any nonzero number raised to the zero power equals 1.

Question 14

Simplify: 2^4 x 3^4

Accepted Answer

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.

Question 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.

Accepted Answer

The expression is 2^6, which equals 64. Doubling every hour means multiplying by 2 six times.

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Properties of Exponents

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