Math / Numbers & Operations

QuestionSolve the problem. 11) $7^{2}$ 12) $6^{3}$ 13) $2^{2}$ 14) $4^{2}$ 15) $4^{3}$ 16) What is 7 cubed? 17) What is 8 to the power of two? 18) What is 5 cubed? 19) What is 6 cubed? 20) What is 4 to the power of three?

Studdy Solution

STEP 1

What is this asking? We need to calculate a bunch of exponents, which is just repeated multiplication! Watch out! Don't mix up the base and the exponent!
The exponent tells you how many times to multiply the base by itself.

STEP 2

1. Seven Squared
2. Six Cubed
3. Two Squared
4. Four Squared
5. Four Cubed
6. Seven Cubed
7. Eight Squared
8. Five Cubed
9. Six Cubed (again!)
10. Four Cubed (again!)

STEP 3

We're asked to find $7^2$ , which means $7$ multiplied by itself two times.

STEP 4

Let's calculate it: $7^2 = 7 \cdot 7 = \textbf{49}$

STEP 5

$6^3$ means multiplying $6$ by itself three times.

STEP 6

Calculation: $6^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}$

STEP 7

$2^2$ is simply $2$ times itself.

STEP 8

Calculate: $2^2 = 2 \cdot 2 = \textbf{4}$

STEP 9

$4^2$ means $4$ multiplied by itself.

STEP 10

Calculate: $4^2 = 4 \cdot 4 = \textbf{16}$

STEP 11

$4^3$ means multiplying $4$ by itself three times.

STEP 12

Calculate: $4^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}$

STEP 13

"Cubed" means to the power of three, so $7$ cubed is $7^3$ .

STEP 14

Calculate: $7^3 = 7 \cdot 7 \cdot 7 = 49 \cdot 7 = \textbf{343}$

STEP 15

$8$ to the power of two is $8^2$ .

STEP 16

Calculate: $8^2 = 8 \cdot 8 = \textbf{64}$

STEP 17

$5$ cubed is $5^3$ .

STEP 18

Calculate: $5^3 = 5 \cdot 5 \cdot 5 = 25 \cdot 5 = \textbf{125}$

STEP 19

We already did this one!
It's $6^3$ .

STEP 20

Calculate (again!): $6^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}$

STEP 21

We've seen this before too!
It's $4^3$ .

STEP 22

Calculate (again!): $4^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}$

STEP 23

$7^2 = 49$ , $6^3 = 216$ , $2^2 = 4$ , $4^2 = 16$ , $4^3 = 64$ , $7$ cubed is $343$ , $8$ to the power of two is $64$ , $5$ cubed is $125$ , $6$ cubed is $216$ , and $4$ to the power of three is $64$ .

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QuestionSolve the problem. 11) 727^{2}72 12) 636^{3}63 13) 222^{2}22 14) 424^{2}42 15) 434^{3}43 16) What is 7 cubed? 17) What is 8 to the power of two? 18) What is 5 cubed? 19) What is 6 cubed? 20) What is 4 to the power of three?

Studdy Solution

STEP 1

What is this asking? We need to calculate a bunch of exponents, which is just repeated multiplication! Watch out! Don't mix up the *base* and the *exponent*!The exponent tells you how many times to multiply the base by itself.

STEP 2

1. Seven Squared2. Six Cubed3. Two Squared4. Four Squared5. Four Cubed6. Seven Cubed7. Eight Squared8. Five Cubed9. Six Cubed (again!)10. Four Cubed (again!)

STEP 3

We're asked to find 727^272, which means 777 multiplied by itself **two** times.

STEP 4

Let's **calculate** it: 72=7⋅7=497^2 = 7 \cdot 7 = \textbf{49}72=7⋅7=49

STEP 5

636^363 means multiplying 666 by itself **three** times.

STEP 6

**Calculation:** 63=6⋅6⋅6=36⋅6=2166^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}63=6⋅6⋅6=36⋅6=216

STEP 7

222^222 is simply 222 times itself.

STEP 8

**Calculate:** 22=2⋅2=42^2 = 2 \cdot 2 = \textbf{4}22=2⋅2=4

STEP 9

424^242 means 444 multiplied by itself.

STEP 10

**Calculate:** 42=4⋅4=164^2 = 4 \cdot 4 = \textbf{16}42=4⋅4=16

STEP 11

434^343 means multiplying 444 by itself **three** times.

STEP 12

**Calculate:** 43=4⋅4⋅4=16⋅4=644^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}43=4⋅4⋅4=16⋅4=64

STEP 13

"Cubed" means to the power of three, so 777 cubed is 737^373.

STEP 14

**Calculate:** 73=7⋅7⋅7=49⋅7=3437^3 = 7 \cdot 7 \cdot 7 = 49 \cdot 7 = \textbf{343}73=7⋅7⋅7=49⋅7=343

STEP 15

888 to the power of two is 828^282.

STEP 16

**Calculate:** 82=8⋅8=648^2 = 8 \cdot 8 = \textbf{64}82=8⋅8=64

STEP 17

555 cubed is 535^353.

STEP 18

**Calculate:** 53=5⋅5⋅5=25⋅5=1255^3 = 5 \cdot 5 \cdot 5 = 25 \cdot 5 = \textbf{125}53=5⋅5⋅5=25⋅5=125

STEP 19

We already did this one!It's 636^363.

STEP 20

**Calculate (again!):** 63=6⋅6⋅6=36⋅6=2166^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}63=6⋅6⋅6=36⋅6=216

STEP 21

We've seen this before too!It's 434^343.

STEP 22

**Calculate (again!):** 43=4⋅4⋅4=16⋅4=644^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}43=4⋅4⋅4=16⋅4=64

STEP 23

72=497^2 = 4972=49, 63=2166^3 = 21663=216, 22=42^2 = 422=4, 42=164^2 = 1642=16, 43=644^3 = 6443=64, 777 cubed is 343343343, 888 to the power of two is 646464, 555 cubed is 125125125, 666 cubed is 216216216, and 444 to the power of three is 646464.

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QuestionSolve the problem. 11) $7^{2}$ 12) $6^{3}$ 13) $2^{2}$ 14) $4^{2}$ 15) $4^{3}$ 16) What is 7 cubed? 17) What is 8 to the power of two? 18) What is 5 cubed? 19) What is 6 cubed? 20) What is 4 to the power of three?

What is this asking? We need to calculate a bunch of exponents, which is just repeated multiplication! Watch out! Don't mix up the base and the exponent!
The exponent tells you how many times to multiply the base by itself.

1. Seven Squared
2. Six Cubed
3. Two Squared
4. Four Squared
5. Four Cubed
6. Seven Cubed
7. Eight Squared
8. Five Cubed
9. Six Cubed (again!)
10. Four Cubed (again!)

We're asked to find $7^2$ , which means $7$ multiplied by itself two times.

Let's calculate it: $7^2 = 7 \cdot 7 = \textbf{49}$

$6^3$ means multiplying $6$ by itself three times.

Calculation: $6^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}$

$2^2$ is simply $2$ times itself.

Calculate: $2^2 = 2 \cdot 2 = \textbf{4}$

$4^2$ means $4$ multiplied by itself.

Calculate: $4^2 = 4 \cdot 4 = \textbf{16}$

$4^3$ means multiplying $4$ by itself three times.

Calculate: $4^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}$

"Cubed" means to the power of three, so $7$ cubed is $7^3$ .

Calculate: $7^3 = 7 \cdot 7 \cdot 7 = 49 \cdot 7 = \textbf{343}$

$8$ to the power of two is $8^2$ .

Calculate: $8^2 = 8 \cdot 8 = \textbf{64}$

$5$ cubed is $5^3$ .

Calculate: $5^3 = 5 \cdot 5 \cdot 5 = 25 \cdot 5 = \textbf{125}$

We already did this one!
It's $6^3$ .

Calculate (again!): $6^3 = 6 \cdot 6 \cdot 6 = 36 \cdot 6 = \textbf{216}$

We've seen this before too!
It's $4^3$ .

Calculate (again!): $4^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = \textbf{64}$

$7^2 = 49$ , $6^3 = 216$ , $2^2 = 4$ , $4^2 = 16$ , $4^3 = 64$ , $7$ cubed is $343$ , $8$ to the power of two is $64$ , $5$ cubed is $125$ , $6$ cubed is $216$ , and $4$ to the power of three is $64$ .