Which of the following is an equivalent expression to (2−3 ⋅93)−429 ⋅9−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)
Responses
23 ⋅92
2 cubed times 9 squared
212⋅9−1229⋅9−10
Start fraction 2 superscript 12 baseline times 9 superscript negative 12 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction
2−7⋅9−129⋅9−10
Start fraction 2 superscript negative 7 baseline times 9 superscript negative 1 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction
2392
The equivalent expression with only positive exponents is: 23 ⋅ 92
To simplify the expression (2−3 ⋅ 93)−429 ⋅9−10 using the properties of integer exponents, we can start by simplifying each factor separately.
First, we simplify the term 2−3 ⋅ 93. The exponent -3 means the reciprocal of 2 cubed, which is 1/23. So, 2−3 can be written as 1/8. The term 93 means 9 squared, which is 92. Therefore, 2−3 ⋅ 93 simplifies to (1/8) * 92.
Next, we simplify the term 429 ⋅ 9−10. The exponent -10 means the reciprocal of 9 raised to the power of 10, which is 1/910. So, 9−10 can be written as 1/910. Therefore, 429 ⋅ 9−10 simplifies to 429 * (1/910).
Combining these simplified terms, we have (1/8) * 92 - 429 * (1/910).
To find an equivalent expression with only positive exponents, we can rewrite the fractions with positive exponents. The reciprocal of 1/8 is 8, and the reciprocal of 1/910 is 910. So, our expression becomes 8 ⋅ 92 - 429 ⋅ 910.
Therefore, an equivalent expression with only positive exponents is 23⋅92.