Free Year 9 Exponent laws Practice | Skillo

Question 1 — Easy

Anika is preparing a presentation about the Great Barrier Reef and uses the expression 5^0 + 2^3 × 2^2 to represent a data calculation. What is the value of this expression?

Answer: First simplify 5^0 = 1, since any non-zero base raised to the power of zero equals 1. Then simplify 2^3 × 2^2 = 2^(3+2) = 2^5 = 32. Adding these gives 1 + 32 = 33. Option A ignores the 5^0 term. Option C treats 5^0 as 5^0 = 5 and 2^5 = 1020, showing confusion about zero exponents. Option D treats 5^0 as 5 and adds 5 + 2^3 × 2^2 = 5 + 32 + 3 erroneously.

Question 2 — Medium

Priya is calculating the storage capacity of a server at her school's computer lab. She simplifies the expression 3^5 × 3^2. What is the correct simplified form using a single base and exponent?

Answer: When multiplying two powers with the same base, you add the exponents: 3^5 × 3^2 = 3^(5+2) = 3^7. Option A is wrong because 5 × 2 = 10, not 5 + 2. Option B is wrong because the base stays as 3, not 9. Option D is wrong because 5 − 2 = 3, which applies the division law instead.

Question 3 — Hard

Zac is tracking the population growth of kangaroos in a wildlife sanctuary. He writes the expression 6^8 ÷ 6^3 to model a ratio. What is the simplified form of this expression?

Answer: When dividing two powers with the same base, you subtract the exponents: 6^8 ÷ 6^3 = 6^(8−3) = 6^5. Option B results from adding the exponents, which applies the multiplication law. Option C incorrectly subtracts the bases instead of keeping them the same. Option D results from multiplying the exponents, which is the power-of-a-power law.