Solved on Feb 06, 2024

Solve: $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ , $2 \times 10^{-15}$ , $2 \times 10^{17}$ , $2 \times 10^{11}$ , undefined.

STEP 1

Assumptions
1. We are given the expression $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ .
2. We need to simplify the expression using the laws of exponents and multiplication/division of numbers.

STEP 2

First, we will multiply the numerical coefficients and then separately multiply the powers of 10.
$\left(3 \times 4\right) \times \left(10^{9} \times 10^{5}\right) / \left(6 \times 10^{-3}\right)$

STEP 3

Multiply the numerical coefficients.
$3 \times 4 = 12$

STEP 4

Now, we will use the law of exponents which states that $a^{m} \times a^{n} = a^{m+n}$ to multiply the powers of 10.
$10^{9} \times 10^{5} = 10^{9+5} = 10^{14}$

STEP 5

Combine the results from STEP_3 and STEP_4.
$12 \times 10^{14}$

STEP 6

Next, we will divide the result by the denominator, starting with the numerical coefficient.
$12 / 6 = 2$

STEP 7

Now, we will use the law of exponents which states that $a^{m} / a^{n} = a^{m-n}$ to divide the powers of 10.
$10^{14} / 10^{-3} = 10^{14 - (-3)} = 10^{14 + 3} = 10^{17}$

STEP 8

Combine the results from STEP_6 and STEP_7.
$2 \times 10^{17}$
The simplified result of the given expression is $2 \times 10^{17}$ .

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Solve: $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ , $2 \times 10^{-15}$ , $2 \times 10^{17}$ , $2 \times 10^{11}$ , undefined.

STEP 1

Assumptions
1. We are given the expression $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ .
2. We need to simplify the expression using the laws of exponents and multiplication/division of numbers.

STEP 2

First, we will multiply the numerical coefficients and then separately multiply the powers of 10.
$\left(3 \times 4\right) \times \left(10^{9} \times 10^{5}\right) / \left(6 \times 10^{-3}\right)$

STEP 3

Multiply the numerical coefficients.
$3 \times 4 = 12$

STEP 4

Now, we will use the law of exponents which states that $a^{m} \times a^{n} = a^{m+n}$ to multiply the powers of 10.
$10^{9} \times 10^{5} = 10^{9+5} = 10^{14}$

STEP 5

Combine the results from STEP_3 and STEP_4.
$12 \times 10^{14}$

STEP 6

Next, we will divide the result by the denominator, starting with the numerical coefficient.
$12 / 6 = 2$

STEP 7

Now, we will use the law of exponents which states that $a^{m} / a^{n} = a^{m-n}$ to divide the powers of 10.
$10^{14} / 10^{-3} = 10^{14 - (-3)} = 10^{14 + 3} = 10^{17}$

STEP 8

Combine the results from STEP_6 and STEP_7.
$2 \times 10^{17}$
The simplified result of the given expression is $2 \times 10^{17}$ .

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Solve: (3×109)(4×105)/(6×10−3)\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)(3×109)(4×105)/(6×10−3), 2×10−152 \times 10^{-15}2×10−15, 2×10172 \times 10^{17}2×1017, 2×10112 \times 10^{11}2×1011, undefined.

STEP 1

Assumptions1. We are given the expression (3×109)(4×105)/(6×10−3)\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)(3×109)(4×105)/(6×10−3).2. We need to simplify the expression using the laws of exponents and multiplication/division of numbers.

STEP 2

First, we will multiply the numerical coefficients and then separately multiply the powers of 10.(3×4)×(109×105)/(6×10−3)\left(3 \times 4\right) \times \left(10^{9} \times 10^{5}\right) / \left(6 \times 10^{-3}\right)(3×4)×(109×105)/(6×10−3)

STEP 3

Multiply the numerical coefficients.3×4=123 \times 4 = 123×4=12

STEP 4

Now, we will use the law of exponents which states that am×an=am+na^{m} \times a^{n} = a^{m+n}am×an=am+n to multiply the powers of 10.109×105=109+5=101410^{9} \times 10^{5} = 10^{9+5} = 10^{14}109×105=109+5=1014

STEP 5

Combine the results from STEP_3 and STEP_4.12×101412 \times 10^{14}12×1014

STEP 6

Next, we will divide the result by the denominator, starting with the numerical coefficient.12/6=212 / 6 = 212/6=2

STEP 7

Now, we will use the law of exponents which states that am/an=am−na^{m} / a^{n} = a^{m-n}am/an=am−n to divide the powers of 10.1014/10−3=1014−(−3)=1014+3=101710^{14} / 10^{-3} = 10^{14 - (-3)} = 10^{14 + 3} = 10^{17}1014/10−3=1014−(−3)=1014+3=1017

STEP 8

Combine the results from STEP_6 and STEP_7.2×10172 \times 10^{17}2×1017The simplified result of the given expression is 2×10172 \times 10^{17}2×1017.

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Solve: $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ , $2 \times 10^{-15}$ , $2 \times 10^{17}$ , $2 \times 10^{11}$ , undefined.

Assumptions
1. We are given the expression $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ .
2. We need to simplify the expression using the laws of exponents and multiplication/division of numbers.

First, we will multiply the numerical coefficients and then separately multiply the powers of 10.
$\left(3 \times 4\right) \times \left(10^{9} \times 10^{5}\right) / \left(6 \times 10^{-3}\right)$

Multiply the numerical coefficients.
$3 \times 4 = 12$

Now, we will use the law of exponents which states that $a^{m} \times a^{n} = a^{m+n}$ to multiply the powers of 10.
$10^{9} \times 10^{5} = 10^{9+5} = 10^{14}$

Combine the results from STEP_3 and STEP_4.
$12 \times 10^{14}$

Next, we will divide the result by the denominator, starting with the numerical coefficient.
$12 / 6 = 2$

Now, we will use the law of exponents which states that $a^{m} / a^{n} = a^{m-n}$ to divide the powers of 10.
$10^{14} / 10^{-3} = 10^{14 - (-3)} = 10^{14 + 3} = 10^{17}$

Combine the results from STEP_6 and STEP_7.
$2 \times 10^{17}$
The simplified result of the given expression is $2 \times 10^{17}$ .