QuestionCalculate $\frac{\left(4 \times 10^{-5}\right)^{2}}{\left(2 \times 10^{6}\right)^{3}}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{\left(4 \times10^{-5}\right)^{}}{\left( \times10^{6}\right)^{3}}$ . . We need to simplify this expression.

STEP 2

First, let's simplify the numerator and the denominator separately.In the numerator, we have $\left(4 \times10^{-5}\right)^{2}$ .To simplify this, we can use the rule $(ab)^2 = a^2 \times b^2$ .
$\left(4 \times10^{-5}\right)^{2} =4^2 \times \left(10^{-5}\right)^2$

STEP 3

Now, calculate the value of $^2$ and $\left(10^{-5}\right)^2$ .
$^2 =16$ $\left(10^{-5}\right)^2 =10^{-10}$ So, $\left( \times10^{-5}\right)^{2} =16 \times10^{-10}$ .

STEP 4

Next, let's simplify the denominator, which is $\left(2 \times10^{6}\right)^{3}$ .
Again, we can use the rule $(ab)^n = a^n \times b^n$ .
$\left(2 \times10^{6}\right)^{3} =2^3 \times \left(10^{6}\right)^3$

STEP 5

Now, calculate the value of $2^3$ and $\left(10^{}\right)^3$ .
$2^3 =8$ $\left(10^{}\right)^3 =10^{18}$ So, $\left(2 \times10^{}\right)^{3} =8 \times10^{18}$ .

STEP 6

Now, substitute the simplified numerator and denominator back into the original expression.
$\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} = \frac{16 \times10^{-10}}{8 \times10^{18}}$

STEP 7

We can simplify this further by dividing the coefficients (16 and) and subtracting the exponents of10 (-10 and18).
$\frac{16 \times10^{-10}}{ \times10^{18}} =2 \times10^{-28}$ So, $\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} =2 \times10^{-28}$ .

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QuestionCalculate $\frac{\left(4 \times 10^{-5}\right)^{2}}{\left(2 \times 10^{6}\right)^{3}}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{\left(4 \times10^{-5}\right)^{}}{\left( \times10^{6}\right)^{3}}$ . . We need to simplify this expression.

STEP 2

First, let's simplify the numerator and the denominator separately.In the numerator, we have $\left(4 \times10^{-5}\right)^{2}$ .To simplify this, we can use the rule $(ab)^2 = a^2 \times b^2$ .
$\left(4 \times10^{-5}\right)^{2} =4^2 \times \left(10^{-5}\right)^2$

STEP 3

Now, calculate the value of $^2$ and $\left(10^{-5}\right)^2$ .
$^2 =16$ $\left(10^{-5}\right)^2 =10^{-10}$ So, $\left( \times10^{-5}\right)^{2} =16 \times10^{-10}$ .

STEP 4

Next, let's simplify the denominator, which is $\left(2 \times10^{6}\right)^{3}$ .
Again, we can use the rule $(ab)^n = a^n \times b^n$ .
$\left(2 \times10^{6}\right)^{3} =2^3 \times \left(10^{6}\right)^3$

STEP 5

Now, calculate the value of $2^3$ and $\left(10^{}\right)^3$ .
$2^3 =8$ $\left(10^{}\right)^3 =10^{18}$ So, $\left(2 \times10^{}\right)^{3} =8 \times10^{18}$ .

STEP 6

Now, substitute the simplified numerator and denominator back into the original expression.
$\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} = \frac{16 \times10^{-10}}{8 \times10^{18}}$

STEP 7

We can simplify this further by dividing the coefficients (16 and) and subtracting the exponents of10 (-10 and18).
$\frac{16 \times10^{-10}}{ \times10^{18}} =2 \times10^{-28}$ So, $\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} =2 \times10^{-28}$ .

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QuestionCalculate (4×10−5)2(2×106)3\frac{\left(4 \times 10^{-5}\right)^{2}}{\left(2 \times 10^{6}\right)^{3}}(2×106)3(4×10−5)2​.

Studdy Solution

STEP 1

Assumptions1. We are given the expression (4×10−5)(×106)3\frac{\left(4 \times10^{-5}\right)^{}}{\left( \times10^{6}\right)^{3}}(×106)3(4×10−5)​. . We need to simplify this expression.

STEP 2

STEP 3

Now, calculate the value of 2^22 and (10−5)2\left(10^{-5}\right)^2(10−5)2.2=16^2 =162=16(10−5)2=10−10\left(10^{-5}\right)^2 =10^{-10}(10−5)2=10−10So, (×10−5)2=16×10−10\left( \times10^{-5}\right)^{2} =16 \times10^{-10}(×10−5)2=16×10−10.

STEP 4

Next, let's simplify the denominator, which is (2×106)3\left(2 \times10^{6}\right)^{3}(2×106)3.Again, we can use the rule (ab)n=an×bn(ab)^n = a^n \times b^n(ab)n=an×bn.(2×106)3=23×(106)3\left(2 \times10^{6}\right)^{3} =2^3 \times \left(10^{6}\right)^3(2×106)3=23×(106)3

STEP 5

Now, calculate the value of 232^323 and (10)3\left(10^{}\right)^3(10)3.23=82^3 =823=8(10)3=1018\left(10^{}\right)^3 =10^{18}(10)3=1018So, (2×10)3=8×1018\left(2 \times10^{}\right)^{3} =8 \times10^{18}(2×10)3=8×1018.

STEP 6

Now, substitute the simplified numerator and denominator back into the original expression.(4×10−5)2(2×106)3=16×10−108×1018\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} = \frac{16 \times10^{-10}}{8 \times10^{18}}(2×106)3(4×10−5)2​=8×101816×10−10​

STEP 7

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QuestionCalculate $\frac{\left(4 \times 10^{-5}\right)^{2}}{\left(2 \times 10^{6}\right)^{3}}$ .

Assumptions1. We are given the expression $\frac{\left(4 \times10^{-5}\right)^{}}{\left( \times10^{6}\right)^{3}}$ . . We need to simplify this expression.

Now, calculate the value of $^2$ and $\left(10^{-5}\right)^2$ .
$^2 =16$ $\left(10^{-5}\right)^2 =10^{-10}$ So, $\left( \times10^{-5}\right)^{2} =16 \times10^{-10}$ .

Next, let's simplify the denominator, which is $\left(2 \times10^{6}\right)^{3}$ .
Again, we can use the rule $(ab)^n = a^n \times b^n$ .
$\left(2 \times10^{6}\right)^{3} =2^3 \times \left(10^{6}\right)^3$

Now, calculate the value of $2^3$ and $\left(10^{}\right)^3$ .
$2^3 =8$ $\left(10^{}\right)^3 =10^{18}$ So, $\left(2 \times10^{}\right)^{3} =8 \times10^{18}$ .

Now, substitute the simplified numerator and denominator back into the original expression.
$\frac{\left(4 \times10^{-5}\right)^{2}}{\left(2 \times10^{6}\right)^{3}} = \frac{16 \times10^{-10}}{8 \times10^{18}}$