Algebra 2
5 marks · HardLet , , and be positive numbers. Given that can be written as , find the values of , , and . Show all your working.
Expand and simplify .
Expand and simplify .
Simplify the entire expression by dividing your answers to parts (a) and (b).
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) a^4b^6
(b) a^3b^{12}c^3
(c) a^{4-3}b^{6-12}c^{-3}=a^1b^{-6}c^{-3}
Common mistakes: Not multiplying exponents correctly; Incorrectly applying laws when dividing
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Applies power of a power law correctly.
M1 (b) · 1 mark · Applies powers to each part inside the bracket correctly.
M2 (c) · 2 marks · Divides exponents using index laws correctly for all variables.
A1 (c) · 1 mark · All values found correctly: m = 1, n = -6, p = -3.
Worked solution
a) Expand
b) Expand
c) Divide exponents: