Solved on Mar 07, 2024

Find the value of $\left(0.1\right)^{5}$ .

STEP 1

Assumptions
1. We need to calculate the value of $(0.1)^{5}$ .
2. The base of the exponentiation is $0.1$ .
3. The exponent is $5$ .

STEP 2

Understand the exponentiation operation. Raising a number to an exponent means multiplying the number by itself the number of times indicated by the exponent.
$a^n = a \times a \times \ldots \times a \quad \text{(n times)}$

STEP 3

Apply the exponentiation operation to $0.1$ raised to the power of $5$ .
$(0.1)^5 = 0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1$

STEP 4

Multiply the first two factors.
$0.1 \times 0.1 = 0.01$

STEP 5

Multiply the result from STEP_4 by the next factor.
$0.01 \times 0.1 = 0.001$

STEP 6

Multiply the result from STEP_5 by the next factor.
$0.001 \times 0.1 = 0.0001$

STEP 7

Multiply the result from STEP_6 by the final factor.
$0.0001 \times 0.1 = 0.00001$

STEP 8

Conclude that the value of $(0.1)^{5}$ is $0.00001$ .
The correct answer is $0.00001$ .

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Find the value of $\left(0.1\right)^{5}$ .

STEP 1

Assumptions
1. We need to calculate the value of $(0.1)^{5}$ .
2. The base of the exponentiation is $0.1$ .
3. The exponent is $5$ .

STEP 2

Understand the exponentiation operation. Raising a number to an exponent means multiplying the number by itself the number of times indicated by the exponent.
$a^n = a \times a \times \ldots \times a \quad \text{(n times)}$

STEP 3

Apply the exponentiation operation to $0.1$ raised to the power of $5$ .
$(0.1)^5 = 0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1$

STEP 4

Multiply the first two factors.
$0.1 \times 0.1 = 0.01$

STEP 5

Multiply the result from STEP_4 by the next factor.
$0.01 \times 0.1 = 0.001$

STEP 6

Multiply the result from STEP_5 by the next factor.
$0.001 \times 0.1 = 0.0001$

STEP 7

Multiply the result from STEP_6 by the final factor.
$0.0001 \times 0.1 = 0.00001$

STEP 8

Conclude that the value of $(0.1)^{5}$ is $0.00001$ .
The correct answer is $0.00001$ .

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Find the value of (0.1)5\left(0.1\right)^{5}(0.1)5.

STEP 1

Assumptions1. We need to calculate the value of (0.1)5(0.1)^{5}(0.1)5.2. The base of the exponentiation is 0.10.10.1.3. The exponent is 555.

STEP 2

Understand the exponentiation operation. Raising a number to an exponent means multiplying the number by itself the number of times indicated by the exponent.an=a×a×…×a(n times)a^n = a \times a \times \ldots \times a \quad \text{(n times)}an=a×a×…×a(n times)

STEP 3

Apply the exponentiation operation to 0.10.10.1 raised to the power of 555.(0.1)5=0.1×0.1×0.1×0.1×0.1(0.1)^5 = 0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1(0.1)5=0.1×0.1×0.1×0.1×0.1

STEP 4

Multiply the first two factors.0.1×0.1=0.010.1 \times 0.1 = 0.010.1×0.1=0.01

STEP 5

Multiply the result from STEP_4 by the next factor.0.01×0.1=0.0010.01 \times 0.1 = 0.0010.01×0.1=0.001

STEP 6

Multiply the result from STEP_5 by the next factor.0.001×0.1=0.00010.001 \times 0.1 = 0.00010.001×0.1=0.0001

STEP 7

Multiply the result from STEP_6 by the final factor.0.0001×0.1=0.000010.0001 \times 0.1 = 0.000010.0001×0.1=0.00001

STEP 8

Conclude that the value of (0.1)5(0.1)^{5}(0.1)5 is 0.000010.000010.00001.The correct answer is 0.000010.000010.00001.

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Find the value of $\left(0.1\right)^{5}$ .

Assumptions
1. We need to calculate the value of $(0.1)^{5}$ .
2. The base of the exponentiation is $0.1$ .
3. The exponent is $5$ .

Understand the exponentiation operation. Raising a number to an exponent means multiplying the number by itself the number of times indicated by the exponent.
$a^n = a \times a \times \ldots \times a \quad \text{(n times)}$

Apply the exponentiation operation to $0.1$ raised to the power of $5$ .
$(0.1)^5 = 0.1 \times 0.1 \times 0.1 \times 0.1 \times 0.1$

Multiply the first two factors.
$0.1 \times 0.1 = 0.01$

Multiply the result from STEP_4 by the next factor.
$0.01 \times 0.1 = 0.001$

Multiply the result from STEP_5 by the next factor.
$0.001 \times 0.1 = 0.0001$

Multiply the result from STEP_6 by the final factor.
$0.0001 \times 0.1 = 0.00001$

Conclude that the value of $(0.1)^{5}$ is $0.00001$ .
The correct answer is $0.00001$ .