Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Independent Practice
Page 9 Exercise 1 Answer
How many times 4 is use as a factor in the expression \(4^{5}\)
Since exponent = 5$
So, 4 is used 5 times as a factor in the expression \(4^{5}\)
Write the numerical expression as repeated multiplication.
\(4^{5}\)= 4 × 4 × 4 × 4 × 4 = 1024
Result
5 times
4 × 4 × 4 × 4 × 4
Page 9 Exercise 2 Answer
Write any power then evaluate the power.
\(2^{3}\)= 2 × 2 × 2 = 4 × 2 = 8
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Result
\(2^{3}\) = 2 × 2 × 2 = 8
Page 9 Exercise 3 Answer
81 = 3 × 3 × 3 × 3 Write 81 as a repeated multiplication of 3s
81 = 3 x 3 x 3 x 3 = \(3^{4}\) Write as a power
Result
3 × 3 × 3 × 3
\(3^{4}\)Page 9 Exercise 4 Answer
\(\left(\frac{1}{2}\right)^3\) Exponent = 3
= \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\) Write as repeated multiplication
Result
\(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\)Page 9 Exercise 5 Answer
9 × 9 × 9 × 9
9 is used 4 times as a factor.
Exponent = 4
Result
Exponent = 4
Page 9 Exercise 6 Answer
\(1.2^{9}\)1.2 is used 9 times as a factor.
Exponent = 9
Result
Exponent = 9
Page 9 Exercise 7 Answer
\(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\)\(\frac{1}{6}\) is used 3 times as a factor.
Exponent = 3
Result
Exponent = 3
Page 9 Exercise 8 Answer
\(0.6^{2}\) Evaluate
= 0.6 × 0.6 Write as repeated multiplication
= 0.36 Multiply
Result
0.36
Page 9 Exercise 9 Answer
\(\left(\frac{1}{4}\right)^2\) Evaluate
= \(\frac{1}{4} \times \frac{1}{4}\) Write as repeated multiplication
= \(\frac{1}{16}\) Multiply
Result
\(\frac{1}{16}\)Page 9 Exercise 10 Answer
\(2^{7}\) Evaluate
= 2 × 2 × 2 × 2 × 2 × 2 × 2 Write as repeated multiplication
= 128 Multiply
Result
128
Page 10 Exercise 12 Answer
\(2^{5}\)base = 2 ; exponent = 5
\(2^{5}\) = 2 × 2 × 2 × 2 × 2 = 32
\(5^{2}\)base = 5 ; exponent = 2
\(5^{2}\) = 5 × 5 = 25
Result
\(2^{5}\) = 32 ; \(5^{2}\) = 25
Page 10 Exercise 13 Answer
Her response was incorrect because
\(\left(8 \times 10^3\right) \times 5^2=8000 \times 25\)80000 × 25
= \(8 \times 10^4 \times 5^2\)
= \(2^3 \times 10^4 \times 5^2\)
Result
\(2^3 \times 10^4 \times 5^2\)Page 10 Exercise 14 Answer
\(0.3^{3}\) Evaluate
= 0.3 × 0.3 × 0.3 Write as repeated multiplication
= 0.027 Multiply
Result
n = 0.027
Page 10 Exercise 15 Answer
1,000,000 = \(10^{6}\)
10 is used as a base because 10 is multiplied repeatedly 6 times as a factor.
Result
Because 10 is repeatedly multiplied
Page 10 Exercise 16 Answer
Zach invested $50 and tripled his money in two years.
$50 × 3 = $150
Kayla invested $50 and after two years, the amount was equal to 50 to the third power.
\(50^{3}\) = 50 × 50 × 50 = $125000
After two years Kayla had more money.
Result
Kayla had more money.
Page 10 Exercise 17 Answer
A) \(2^{10}\)
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 1024
B) 5 x 5 x 5 x 5
= 625
C) \(4^{5}\)
= 4 x 4 x 4 x 4 x 4
= 1024
D) 4 x 4 x 4 x 4 x 4
= 1024
The expression 5 x 5 x 5 x 5 is Not equal to 1024
Result
5 x 5 x 5 x 5
Page 10 Exercise 18 Answer
A) \(\frac{1}{3} \times \frac{1}{6}\)
= \(\frac{1}{18}\)
B) \(\frac{1}{4} \times\left(\frac{1}{3}\right)^3\)
= \(\frac{1}{4} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\)
= \(\frac{1}{108}\)
C) \(\left(\frac{1}{2}\right)^2 \times\left(\frac{1}{3}\right)^2\)
= \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{3} \times \frac{1}{3}\)
= \(\frac{1}{4} \times \frac{1}{9}\)
= \(\frac{1}{36}\)
D) \(\frac{1}{2} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\)
= \(\frac{1}{2} \times \frac{1}{27}\)
= \(\frac{1}{54}\)
The expression \(\left(\frac{1}{2}\right)^2 \times\left(\frac{1}{3}\right)^2\) is equal to \(\frac{1}{36}\)
Result
\(\left(\frac{1}{2}\right)^2 \times\left(\frac{1}{3}\right)^2\)