Pack B — Fluency

Mathematics

Year 10 · Exponents and Indices

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

SilverQuestions 11–20

11.
Simplify $2 x^{{p}} \times 5 x^{{q}}$ .
12.
Simplify $\dfrac{{c1} x^{{p}}}{{c2} x^{{q}}}$ .
13.
Simplify $\left(\dfrac{x^{{a}}}{x^{{b}}}\right)^{{n}}$ .
14.
Simplify $x^{{a}} \times x^{-{b}}$ .
15.
Write $\dfrac{1}{x^{{n}}}$ using a negative index.
16.
Calculate $(4 \times 10^{{p}}) \times (5 \times 10^{{q}})$ , giving your answer in standard form.
17.
Calculate $\dfrac{{a} \times 10^{{p}}}{{b} \times 10^{{q}}}$ in standard form.
18.
Simplify $\dfrac{x^{{a}} \times x^{{b}}}{x^{{c}}}$ .
19.
How many times larger is $6 \times 10^{{p}}$ than $2 \times 10^{{q}}$ ?
20.
Simplify $(-2 x^{{p}})^{{n}}$ .

GoldQuestions 21–30

PlatinumQuestions 31–40

31.
Solve $2^{x+1} = 64$ .
32.
Solve $3^{2x} = 729$ .
33.
Simplify $\dfrac{({c} x^{{a}})^{{n}} \cdot x^{{b}}}{x^{{c2}}}$ .
34.
The mass of Earth is $6 \times 10^{24}$ kg and the mass of the Sun is $2 \times 10^{{p}}$ kg. How many times more massive is the Sun?
35.
Simplify $\dfrac{x^{{a}} \cdot y^{-{b}}}{x^{-{c}} \cdot y^{{d}}}$ , expressing the answer with positive indices.
36.
Evaluate $(81)^{3/4}$ .
37.
Light travels at $3 \times 10^8$ m/s. Calculate the distance light travels in $200$ seconds, in standard form.
38.
Solve $2^{x} \cdot 2^{x+1} = 128$ .
39.
Simplify $\left(\dfrac{{c}x^{{a}}y^{{b}}}{x^{{c2}}y^{{d}}}\right)^{{n}}$ .
40.
Solve $x^{1/3} = 5$ for positive $x$ .