Answer :
Therefore, the expression [tex]\(\left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right)^3\)[/tex] simplified as a single exponent is [tex]{\left(\frac{1}{10}\right)^5}[/tex].
To simplify [tex]\(\left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right)^3\)[/tex] as a single exponent, follow these steps:
First, express the given expression in terms of powers of [tex]\(\frac{1}{10}\):\left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right)^3[/tex]
Notice that [tex]\(\left(\frac{1}{10}\right)\) and \(\left(\frac{1}{10}\right)\)[/tex] can each be written as [tex]\(\left(\frac{1}{10}\right)^1\):\left(\frac{1}{10}\right)^1 \times \left(\frac{1}{10}\right)^1 \times \left(\frac{1}{10}\right)^3[/tex]
When multiplying powers with the same base, you add the exponents. Thus:
[tex]\left(\frac{1}{10}\right)^1 \times \left(\frac{1}{10}\right)^1 \times \left(\frac{1}{10}\right)^3 = \left(\frac{1}{10}\right)^{1+1+3}[/tex]
Simplify the exponents:
[tex]\left(\frac{1}{10}\right)^{1+1+3} = \left(\frac{1}{10}\right)^5[/tex]
Therefore, the expression [tex]\(\left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right) \times \left(\frac{1}{10}\right)^3\)[/tex] simplified as a single exponent is:
[tex]\boxed{\left(\frac{1}{10}\right)^5}[/tex]
