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Put the expressions in order from least to greatest. $\newline$ $\newline$ Order Items: $[7^{-5}][7^2 \times 7^3][\frac{1}{7^6}][(7^2)^3]$

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Compare and order decimals

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Q. Put the expressions in order from least to greatest.

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Order Items:

[7^{-5}][7^2 \times 7^3][\frac{1}{7^6}][(7^2)^3]

Simplify Expressions: Step $1$ : Simplify each expression. $\newline$ - Simplify $7^{-5}$ . This is the same as $1/(7^5)$ . $\newline$ - Simplify $7^2 \times 7^3$ . Using the property of exponents, $a^m \times a^n = a^{(m+n)}$ , this becomes $7^{(2+3)} = 7^5$ . $\newline$ - Simplify $1/7^6$ . This remains as it is. $\newline$ - Simplify $(7^2)^3$ . Using the property $(a^m)^n = a^{(m\ast n)}$ , this becomes $7^{(2\ast3)} = 7^6$ .
Compare Values: Step $2$ : Compare the values. $\newline$ - $7^{-5}$ or $1/(7^5)$ is a very small positive number. $\newline$ - $7^5$ is a large positive number. $\newline$ - $1/7^6$ is even smaller than $1/(7^5)$ because the exponent is higher in the denominator. $\newline$ - $7^6$ is larger than $7^5$ .
Order Expressions: Step $3$ : Order the expressions from least to greatest. $\newline$ - $1/7^6$ is the smallest. $\newline$ - $1/(7^5)$ or $7^{-5}$ is next. $\newline$ - $7^5$ follows. $\newline$ - $7^6$ is the largest.

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