iGCSE Mathematics (0580) :E2.4 Use and interpret positive, negative and zero indices.iGCSE Style Questions Paper 2

Question

(a) Simplify fully $(4ab^5)^4$

(b) $2p^{\frac{1}{3}} = 6$. Find the value of $p$.

▶️ Answer/Explanation

Solution

(a) 256a⁴b²⁰

Apply power to each term: 4⁴ = 256, a⁴, (b⁵)⁴ = b²⁰

(b) 27

Divide both sides by 2: p^1/3 = 3

Cube both sides: p = 3³ = 27

(c) 6

Express all terms as powers of 3: 81 = 3⁴, 9 = 3²

Equation becomes (3⁴)² ÷ 3^t = 3²

Simplify: 3^8-t = 3² ⇒ 8-t = 2 ⇒ t = 6

Question

Simplify fully $(216y^{216})^{\frac{2}{3}}$.

▶️ Answer/Explanation

Solution

Ans: $36y^{144}$

First simplify $216^{\frac{2}{3}}$ = $(6^3)^{\frac{2}{3}} = 6^2 = 36$.

Then $(y^{216})^{\frac{2}{3}} = y^{216 \times \frac{2}{3}} = y^{144}$.

Combine both parts to get $36y^{144}$.

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