Solved on Nov 13, 2023

Simplify $\left(5 \times 10^{8}\right)^{4}$ and express the result in scientific notation.

STEP 1

Assumptions1. We are given the expression $(5 \times10^{8})^{4}$ . We need to simplify this expression and write the answer in scientific notation

STEP 2

We can simplify the expression by applying the power of a product property, which states that $(ab)^n = a^n \times b^n$ . $\left(5 \times10^{8}\right)^{4} =5^{4} \times \left(10^{8}\right)^{4}$

STEP 3

Now, we can calculate the value of $5^{}$ and $\left(10^{8}\right)^{}$ .
$5^{} =625$ $\left(10^{8}\right)^{} =10^{32}$

STEP 4

Substitute these values back into the equation.
$\left( \times10^{8}\right)^{4} =625 \times10^{32}$

STEP 5

Now, we need to convert this to scientific notation. Scientific notation is written as $a \times10^{n}$ , where $1 \leq a <10$ and $n$ is an integer.To convert $625$ to a number between $1$ and $10$ , we can write it as $.25 \times10^{2}$ .

STEP 6

Substitute this value back into the equation.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{2} \times10^{32}$

STEP 7

We can simplify this further by using the rule of exponents, which states that $a^{m} \times a^{n} = a^{m+n}$ .
$\left(5 \times10^{}\right)^{4} =6.25 \times10^{2+32}$

STEP 8

Calculate the exponent.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{34}$ So, the simplified expression in scientific notation is $6.25 \times10^{34}$ .

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Simplify $\left(5 \times 10^{8}\right)^{4}$ and express the result in scientific notation.

STEP 1

Assumptions1. We are given the expression $(5 \times10^{8})^{4}$ . We need to simplify this expression and write the answer in scientific notation

STEP 2

We can simplify the expression by applying the power of a product property, which states that $(ab)^n = a^n \times b^n$ . $\left(5 \times10^{8}\right)^{4} =5^{4} \times \left(10^{8}\right)^{4}$

STEP 3

Now, we can calculate the value of $5^{}$ and $\left(10^{8}\right)^{}$ .
$5^{} =625$ $\left(10^{8}\right)^{} =10^{32}$

STEP 4

Substitute these values back into the equation.
$\left( \times10^{8}\right)^{4} =625 \times10^{32}$

STEP 5

Now, we need to convert this to scientific notation. Scientific notation is written as $a \times10^{n}$ , where $1 \leq a <10$ and $n$ is an integer.To convert $625$ to a number between $1$ and $10$ , we can write it as $.25 \times10^{2}$ .

STEP 6

Substitute this value back into the equation.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{2} \times10^{32}$

STEP 7

We can simplify this further by using the rule of exponents, which states that $a^{m} \times a^{n} = a^{m+n}$ .
$\left(5 \times10^{}\right)^{4} =6.25 \times10^{2+32}$

STEP 8

Calculate the exponent.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{34}$ So, the simplified expression in scientific notation is $6.25 \times10^{34}$ .

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Simplify (5×108)4\left(5 \times 10^{8}\right)^{4}(5×108)4 and express the result in scientific notation.

STEP 1

Assumptions1. We are given the expression (5×108)4(5 \times10^{8})^{4}(5×108)4 . We need to simplify this expression and write the answer in scientific notation

STEP 2

We can simplify the expression by applying the power of a product property, which states that (ab)n=an×bn(ab)^n = a^n \times b^n(ab)n=an×bn.(5×108)4=54×(108)4\left(5 \times10^{8}\right)^{4} =5^{4} \times \left(10^{8}\right)^{4} (5×108)4=54×(108)4

STEP 3

Now, we can calculate the value of 55^{}5 and (108)\left(10^{8}\right)^{}(108).5=6255^{} =6255=625(108)=1032\left(10^{8}\right)^{} =10^{32} (108)=1032

STEP 4

Substitute these values back into the equation.(×108)4=625×1032\left( \times10^{8}\right)^{4} =625 \times10^{32} (×108)4=625×1032

STEP 5

Now, we need to convert this to scientific notation. Scientific notation is written as a×10na \times10^{n}a×10n, where 1≤a<101 \leq a <101≤a<10 and nnn is an integer.To convert 625625625 to a number between 111 and 101010, we can write it as .25×102.25 \times10^{2}.25×102.

STEP 6

Substitute this value back into the equation.(5×108)4=6.25×102×1032\left(5 \times10^{8}\right)^{4} =6.25 \times10^{2} \times10^{32} (5×108)4=6.25×102×1032

STEP 7

We can simplify this further by using the rule of exponents, which states that am×an=am+na^{m} \times a^{n} = a^{m+n}am×an=am+n.(5×10)4=6.25×102+32\left(5 \times10^{}\right)^{4} =6.25 \times10^{2+32} (5×10)4=6.25×102+32

STEP 8

Calculate the exponent.(5×108)4=6.25×1034\left(5 \times10^{8}\right)^{4} =6.25 \times10^{34} (5×108)4=6.25×1034So, the simplified expression in scientific notation is 6.25×10346.25 \times10^{34}6.25×1034.

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Simplify $\left(5 \times 10^{8}\right)^{4}$ and express the result in scientific notation.

Assumptions1. We are given the expression $(5 \times10^{8})^{4}$ . We need to simplify this expression and write the answer in scientific notation

We can simplify the expression by applying the power of a product property, which states that $(ab)^n = a^n \times b^n$ . $\left(5 \times10^{8}\right)^{4} =5^{4} \times \left(10^{8}\right)^{4}$

Now, we can calculate the value of $5^{}$ and $\left(10^{8}\right)^{}$ .
$5^{} =625$ $\left(10^{8}\right)^{} =10^{32}$

Substitute these values back into the equation.
$\left( \times10^{8}\right)^{4} =625 \times10^{32}$

Now, we need to convert this to scientific notation. Scientific notation is written as $a \times10^{n}$ , where $1 \leq a <10$ and $n$ is an integer.To convert $625$ to a number between $1$ and $10$ , we can write it as $.25 \times10^{2}$ .

Substitute this value back into the equation.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{2} \times10^{32}$

We can simplify this further by using the rule of exponents, which states that $a^{m} \times a^{n} = a^{m+n}$ .
$\left(5 \times10^{}\right)^{4} =6.25 \times10^{2+32}$

Calculate the exponent.
$\left(5 \times10^{8}\right)^{4} =6.25 \times10^{34}$ So, the simplified expression in scientific notation is $6.25 \times10^{34}$ .