Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Homework And Practice
Page 11 Exercise 1 Answer
\(5^{12}\) = 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5
5 is repeatedly multiplied.
Base = 5
Result
5
Page 11 Exercise 2 Answer
\(1.2^{2}\)= 1.2 × 1.2
1.2 is repeatedly multiplied.
Base = 1.2
Result
1.2
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Page 11 Exercise 3 Answer
\(\left(\frac{1}{3}\right)^4\)
= \(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\)
\(\frac{1}{3}\) is repeatedly multiplied.
Base = \(\frac{1}{3}\)
Result
\(\frac{1}{3}\)Page 11 Exercise 4 Answer
7 × 7 × 7 × 7
= \(7^{4}\)
7 is multiplied 4 times as a factor.
Exponent = 4
Result
4
Page 11 Exercise 5 Answer
\(\left(\frac{2}{3}\right)^8\)\(\frac{2}{3}\) is multiplied 8 times as a factor.
Exponent = 8
Result
8
Page 11 Exercise 6 Answer
0.5 × 0.5 × 0.5
= \(0.5^{3}\)
0.5 is multiplied 3 times as a factor.
Exponent = 3
Result
3
Page 11 Exercise 7 Answer
\(9^{3}\) Evaluate
= 9 x 9 x 9 Write as repeated multiplication
= 729 Multiply
Result
729
Page 11 Exercise 8 Answer
\(\left(\frac{1}{4}\right)^3\) Evaluate
= \(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}\) Write as repeated multiplication
= \(\frac{1}{64}\) Multiply
Result
\(\frac{1}{64}\)Page 11 Exercise 9 Answer
\(3^{5}\) Evaluate
= 3 x 3 x 3 x 3 x 3 Write as repeated multiplication
= 243 Multiply
Result
243
Page 11 Exercise 10 Answer
\(\left(\frac{1}{8}\right)^3\) Evaluate
= \(\frac{1}{8} \times \frac{1}{8} \times \frac{1}{8}\) Write as repeated multiplication
= \(\frac{1}{512}\) Multiply
Result
\(\frac{1}{512}\)Page 11 Exercise 11 Answer
\(99^{9}\) Evaluate
= 1 Any non zero raised to the exponent of 0 has a value of 1
Result
1
Page 11 Exercise 12 Answer
\(1.5^{2}\) Evaluate
= 1.5 × 1.5 Write as repeated multiplication
= 2.25 Multiply
Result
2.25
Page 12 Exercise 13 Answer
\(0.3^{4}\) = 0.3 × 0.3 × 0.3 × 0.3 = 0.0081 Evaluate
\(0.9^{2}\) = 0.9 × 0.9 = 0.81 Evaluate
Result
No \(0.3^{4}\) is NOT equal to \(0.9^{2}\)
Page 12 Exercise 14 Answer
27 = 3 × 3 × 3 × 3 Write as repeated multiplication
27 = \(3^{4}\) Write as power
Result
27 can be written using number 3 as :
3 × 3 × 3 × 3 and \(3^{4}\)
Page 12 Exercise 15 Answer
\(1^{102}\) = 1
The value of any power of 1 is equal to 1.
Example → \(1^{32}=1 ; 1^6=1 ; 1^{100}=1\)
Result
1
Page 12 Exercise 19 Answer
A) \(8^{3}\)
= 8 × 8 × 8
= 512
B) 6 × 6 × 6
= 216
C) \(7^{3}\)
= 7 × 7 × 7
= 343
D) 7 × 7 × 7 × 7
= 2401
Result
\(7^{3}\) is equal to 343
Page 12 Exercise 20 Answer
A) \(0.5^{3}\)
= 0.5 × 0.5 × 0.5
= 0.125
B) 0.5 × 3
= 1.5
C) 0.5 × 0.5 × 0.5
= 0.125
D) \(0.5 \times 0.5^2\)
= 0.5 × 0.5 × 0.5
= 0.125
Result
0.5 × 3 is NOT equal to 0.125