Mathski
Worksheet
Indices I
IB Mathematics AA · SL & HL · Shadow Worksheet
Practice
Name
Question 1
Simplify the following, giving your answers with positive indices:
(a)\(x^3 \cdot x^5\)
(b)\(\dfrac{y^8}{y^3}\)
(c)\((z^4)^3\)
(d)\(x^{-3}\)
(e)\((2x^2)^3\)
(f)\(\dfrac{6x^5 y^3}{3x^2 y}\)
(a)
Answer
\(x^8\)
(b)
Answer
\(y^5\)
(c)
Answer
\(z^{12}\)
(d)
Answer
\(\dfrac{1}{x^3}\)
(e)
Answer
\(8x^6\)
(f)
Answer
\(2x^3 y^2\)
Question 2
Write the following in the form \(2^n\):
(a)\(4^3\)
(b)\(8 imes 4^2\)
(c)\(\dfrac{16^3}{32}\)
(a)
Rewrite
\(4^3 = (2^2)^3\)
Answer
\(2^6\)
(b)
Rewrite
\(8 imes 4^2 = 2^3 imes 2^4\)
Answer
\(2^7\)
(c)
Rewrite
\(\dfrac{(2^4)^3}{2^5} = \dfrac{2^{12}}{2^5}\)
Answer
\(2^7\)
Question 3
Solve the following equations:
(a)\(2^x = 64\)
(b)\(3^{x+1} = 81\)
(c)\(4^x = \dfrac{1}{8}\)
(a)
Write as power of 2
\(2^x = 2^6\)
Answer
\(x = 6\)
(b)
Write as power of 3
\(3^{x+1} = 3^4 \Rightarrow x+1=4\)
Answer
\(x = 3\)
(c)
Rewrite
\(2^{2x} = 2^{-3} \Rightarrow 2x = -3\)
Answer
\(x = -\dfrac{3}{2}\)
Question 4
Simplify, leaving your answer in index form:
(a)\(x^{1/2} \cdot x^{3/2}\)
(b)\(\left(\dfrac{x^3}{x^{-1}} ight)^2\)
(c)\(\dfrac{(3x)^2 \cdot x^{-3}}{9x^4}\)
(a)
Answer
\(x^2\)
(b)
Simplify inner
\(x^{3-(-1)}=x^4\), then \((x^4)^2\)
Answer
\(x^8\)
(c)
Numerator
\(9x^2\cdot x^{-3}=9x^{-1}\)
Answer
\(x^{-5}\)
Question 5
Write the following without negative or fractional indices:
(a)\(x^{1/3}\)
(b)\(x^{-2/3}\)
(c)\(4x^{-1/2}\)
(a)
Answer
\(\sqrt[3]{x}\)
(b)
Answer
\(\dfrac{1}{\sqrt[3]{x^2}}\)
(c)
Answer
\(\dfrac{4}{\sqrt{x}}\)
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