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
2392
Start Fraction 2 cubed over 9 squared end fraction
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
23 ⋅92
2 cubed times 9 squared
2−7⋅9−129⋅9−10
The equivalent expression with only positive exponents is option B: Start Fraction 2 cubed over 9 squared end fraction.
To find the equivalent expression with only positive exponents, we need to apply the properties of integer exponents. Let's break down the expression step by step.
We start with the expression: (2−3 * 93) - 429 * 9−10
Step 1: Simplify the exponents using the product rule and the power rule.
2−3 can be rewritten as 1/2^3
93 can be rewritten as 9^3
9−10 can be rewritten as 1/9^10
The expression becomes: (1/2^3 * 9^3) - 429 * 1/9^10
Step 2: Simplify the expression using the quotient rule.
1/2^3 * 9^3 can be written as (9^3 / 2^3)
1/9^10 can be written as 9^-10
The expression becomes: (9^3 / 2^3) - 429 * 9^-10
Step 3: Simplify the expression by applying the power rule.
9^3 can be written as 3^2 * 3, and 2^3 can be written as 2^2 * 2.
The expression becomes: ((3^2 * 3) / (2^2 * 2)) - 429 * 9^-10
Step 4: Simplify the expression further.
3^2 * 3 can be simplified to 9 * 3, which is equal to 27.
2^2 * 2 can be simplified to 4 * 2, which is equal to 8.
The expression becomes: (27 / 8) - 429 * 9^-10
Step 5: Rewrite 9^-10 as 1/9^10.
The expression becomes: (27 / 8) - 429 * (1/9^10)
So, the equivalent expression with only positive exponents is:
(27 / 8) - 429 / 9^10
Therefore, the correct answer is: Start fraction 27 over 8 minus 429 over 9 to the power of 10 end fraction.