What is the value of n? Use pencil and paper. Explain why the exponent on the left side of the equation is not equal to the sum of the exponents on the right side.
2.8 × 10^13 = (4 × 10^7)(7 × 10^n)
The value of n is __.
What is the value of n? Use pencil and paper. Explain why the exponent on the left side of the equation is not equal to the sum of the exponents on the right side. 2.8 × 10^13 = (4 × 10^7)(7 × 10^n) The value of n is
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To solve for ( n ) in the equation ( 2.8 times 10^{13} = (4 times 10^{7})(7 times 10^{n}) ), we will first simplify the right side of the equation.
1. Multiply the coefficients (the numbers in front):
[
4 times 7 = 28
]
2. Add the exponents for the powers of 10:
[
10^{7} times 10^{n} = 10^{(7+n)}
]
3. So, the equation becomes:
[
2.8 times 10^{13} = 28 times 10^{(7+n)}
]
4. Rewrite ( 28 ) to match the format of ( 2.8 ):
[
28 = 2.8 times 10^{1}
]
Thus, we can rewrite the equation as:
[
2.8 times 10^{13} = 2.8 times 10^{1} times 10^{(7+n)}
]
This simplifies to:
[
2.8 times 10^{13} = 2.8 times 10^{(1 + 7 + n)}
]