How can the pattern of repeated multiplication be extended and expanded, and how can exponential notation be…

Question

How can the pattern of repeated multiplication be extended and expanded, and how can exponential notation be used to calculate the answers?

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the problems:

1. Extend the pattern another 3 times (up the power of 5).

a)

20 \times 20 \times 20 = 20^3

20 \times 20 \times 20 \times 20 = 20^4

20 \times 20 \times 20 \times 20 \times 20 = 20^5

b)

10 \times 10 \times 10 = 10^3

10 \times 10 \times 10 \times 10 = 10^4

10 \times 10 \times 10 \times 10 \times 10 = 10^5

c)

17 \times 17 \times 17 = 17^3

17 \times 17 \times 17 \times 17 = 17^4

17 \times 17 \times 17 \times 17 \times 17 = 17^5

d)

38 \times 38 \times 38 = 38^3

38 \times 38 \times 38 \times 38 = 38^4

38 \times 38 \times 38 \times 38 \times 38 = 38^5

e)

59 \times 59 \times 59 = 59^3

59 \times 59 \times 59 \times 59 = 59^4

59 \times 59 \times 59 \times 59 \times 59 = 59^5

f)

15 \times 15 \times 15 = 15^3

15 \times 15 \times 15 \times 15 = 15^4

15 \times 15 \times 15 \times 15 \times 15 = 15^5

2. Expand the exponential notation and use your calculator to calculate the answer.

a) $22^3$

Expand the notation.
$22^3 = 22 \times 22 \times 22$
Calculate the value.
$22 \times 22 \times 22 = 10648$
The answer is $\boxed{10648}$

b) $81^2$
Expand the notation.
$81^2 = 81 \times 81$
Calculate the value.
$81 \times 81 = 6561$
The answer is $\boxed{6561}$

c) $74^4$
Expand the notation.
$74^4 = 74 \times 74 \times 74 \times 74$
Calculate the value.
$74 \times 74 \times 74 \times 74 = 29986576$
The answer is $\boxed{29986576}$

d) $39^1$
Expand the notation.
$39^1 = 39$
Calculate the value.
$39 = 39$
The answer is $\boxed{39}$

e) $97^7$
Expand the notation.
$97^7 = 97 \times 97 \times 97 \times 97 \times 97 \times 97 \times 97$
Calculate the value.
$97^7 = 80798284478113$
The answer is $\boxed{80798284478113}$

f) $32^8$
Expand the notation.
$32^8 = 32 \times 32 \times 32 \times 32 \times 32 \times 32 \times 32 \times 32$
Calculate the value.
$32^8 = 1099511627776$
The answer is $\boxed{1099511627776}$

How can the pattern of repeated multiplication be extended and expanded, and how can exponential notation be used to calculate the answers?