Put the expressions in order from least to greatest. Order Items: [[7^-5][7^2 * 7^3][1/7^6][(7^2)^3]]

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

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Math Problems

Grade 7

Compare and order decimals

Full solution

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.