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What is \[8\] to the third power times \[8\] to the negative \[10\] power?

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Last updated date: 19th May 2024
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Answer
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Hint:Powers and Indices are other names for exponents. Exponential notation is a form of mathematical shorthand that helps us to express complex expressions in a more concise manner.

Complete step by step answer:
An exponent is a number or letter that is written above and to the right of the base in a mathematical expression. It denotes that the base will be lifted to a certain level of strength.The base is $x$, and the exponent or power is $n$.

Firstly we should multiply exponents with the same base,and then the exponents are added.
So we can take a look at the below answers obtained.
\[{8^3}\,.\,{8^{ - 10}}\, \to \,3 + \,( - 10)\, = \, - 7\, \to \,{8^{ - 7}}\]
\[ = > \,{8^{ - 7}}\]

And hence we successfully found the answer.

A positive exponent indicates how many times a base number should be multiplied, while a negative exponent indicates how many times a base number should be divided. A negative exponent indicates how many times the number should be divided by. We can use the Reciprocal (i.e.\[{\text{1/}}{{\text{a}}^{\text{n}}}\]) to alter the sign of the exponent (plus to minus, or minus to plus). A negative exponent indicates that a basis is on the fraction line's denominator side.

Hence, we found that \[8\] to the third power times \[8\] to the negative \[10\] power is \[{8^{ - 7}}\].

Note: The negative exponent rule states that a negative exponent number should be placed in the denominator and vice versa. Another way to find the exponential is to start with "1" and multiply or divide by the exponent as many times as it says, and you will get the correct answer. For example:
\[{5^2} = \,1\,\, \times \,\,5\, \times \,5\, = \,25\]
\[{5^{ - 1}}\, = \,1\, \div \,5\]